Travel_Word_Problems/231990: A car and a truck leave the same place at the same time. the car is traveling twice as fast as the truck. In three hours time, the car is ahead of the truck by 72 miles. at what rate of speed is each vehicle driving? 1 solutions Answer 171541 by drj(1380) on 2009-10-27 12:04:43 (Show Source):
You can put this solution on YOUR website! A car and a truck leave the same place at the same time. The car is traveling twice as fast as the truck. In three hours time, the car is ahead of the truck by 72 miles. at what rate of speed is each vehicle driving?
Step 1. Let x be the speed of the truck.
Step 2. Let 2x be the speed of the car since it is traveling twice as fast as the truck.
Step 3. Distance= speed * time.
Step 4. Let 3x be the distance traveled by the truck after 3 hours
Step 5. Let 3*2x=6x be the distance traveled by the car after 3 hours.
Step 6. Using Steps 4 and 5, then, 6x-3x=72 since they are 72 miles apart after 3 hours.
Step 7. Solving leads to or or miles per hour. Then miles per hour.
Step 8. ANSWER. The truck is 24 miles per hour and the car is 48 miles per hour.
I hope the above steps were helpful.
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Surface-area/231989: The length of a rectangle is twice its width. If the perimeter of the rectangle is 60 ft , find its area 1 solutions Answer 171540 by drj(1380) on 2009-10-27 11:57:23 (Show Source):
You can put this solution on YOUR website! The length of a rectangle is twice its width. If the perimeter of the rectangle is 60 ft, find its area
Step 1. The perimeter P means adding up all the four sides of a rectangle.
Cartoon (animation) form: For tutors: simplify_cartoon( w+w+2w+2w=60 )
If you have a website, here's a link to this solution.
DETAILED EXPLANATION
Look at . Eliminated similar terms,,, replacing them with It becomes . Look at . Added fractions or integers together It becomes . Look at . Remove unneeded parentheses around factor It becomes . Look at . Moved these terms to the left It becomes . Look at . Solved linear equation equivalent to 6*w-60 =0 It becomes . Result: This is an equation! Solutions: w=10.
Universal Simplifier and Solver
Done!
For w=10 , then 2w=20 and P=2(10+20)=60 which is a true statement.
Step 6. Area A is given as A=length * width = 20*10=200 square feet.
Step 7. ANSWER: The area is 200 square feet.
I hope the above steps were helpful.
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Human-and-algebraic-language/230637: in 2006 the number of americans who were healthclub members was 42.7 million. this was an increase of 106% from the number in 1990. how many americans were members in 1990? 1 solutions Answer 170801 by drj(1380) on 2009-10-23 14:41:09 (Show Source):
You can put this solution on YOUR website! In 2006 the number of Americans who were members of a health club was 42.7 million. This was an increase of 106% from the number of clubs in 1990. How many Americans were health club members in 1990?
Step 1. 106% means 1.06 in decimal form.
Step 2. Let x be the number of Americans who were health club numbers in 1990
Step 3. Let 1.06x be the amount of increase from 1990.
Step 4. Then x+1.06x=42.7 million be the current amount of 42.7.
Step 5. Solving x+1.06x=42.7 yields the following steps
Divide by 2.06 to both sides of the equation
Step 6. ANSWER: The number of club members in 1990 is 20.73 million.
I hope the above steps were helpful.
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Respectfully,
Dr J
Age_Word_Problems/230632: Don is twice as old as Irene; Ed is 16 years older than Irene. The sum of all three of their ages is 60 years. Find the age of each person. 1 solutions Answer 170800 by drj(1380) on 2009-10-23 14:38:31 (Show Source):
You can put this solution on YOUR website! Don is twice as old as Irene; Ed is 16 years older than Irene. The sum of all three of their ages is 60 years. Find the age of each person.
Step 1. Let x be the age of Irene.
Step 2. Let 2x be the age of Don since he'1 twice as old as Irene.
Step 3. Let x+16 be the age of Ed since he's 16 years older than Irene.
Step 4. Then, x+2x+x+16=60 since the sum of their ages is 60.
Step 5. Solving yields the following steps
Subtract 16 from both sides of the equation
Divide by 4 to both sides of the equation
, , . Note the sum of the ages equal to 60 years old.
Step 6. ANSWER: Irene is 11 years old, Don is 22 years old, and Ed is 27 years old.
I hope the above steps were helpful.
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Respectfully,
Dr J
http://www.FreedomUniversity.TV
Probability-and-statistics/230626: In a standard deck of 52 playing cards, what is the probability of drawing a number greater than 10? 1 solutions Answer 170799 by drj(1380) on 2009-10-23 14:33:16 (Show Source):
You can put this solution on YOUR website! In a standard deck of 52 playing cards, what is the probability of drawing a number greater than 10?
Step 1. Assume you call the face cards a number greater than 10.
Step 2. There are 12 face cards in a 52-card deck.
Step 3. ANSWER: Therefore, the probability of drawing a facecard or a number greater than ten is if you assume a facecard is a number. If you don't call the face card a number, there is no number greater than 10 in a 52-card deck. Then the probability of a number greater than 10 is zero.
I hope the above steps were helpful.
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Respectfully,
Dr J
http://www.FreedomUniversity.TV
Probability-and-statistics/230627: In a standard deck of 52 playing cards, what is the probability of drawing a heart, club, diamond, or spade?
You can put this solution on YOUR website! In a standard deck of 52 playing cards, what is the probability of drawing a heart, club, diamond, or spade?
Step 1. There are 13 cards to a suit (heart, club, diamond, or spade).
Step 2. ANSWER: Therefore the probability is
I hope the above steps were helpful.
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Dr J
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Probability-and-statistics/230624: .In a standard deck of 52 playing cards, what is the probability of drawing a face card (J,Q, or K)? 1 solutions Answer 170797 by drj(1380) on 2009-10-23 14:25:24 (Show Source):
You can put this solution on YOUR website! In a standard deck of 52 playing cards, what is the probability of drawing a face card (J,Q, or K)?
Step 1. There are a total of 12 face cards in a standard 52-card deck.
Step 2. Therefore the probability is P(face card)=
Step 3. ANSWER: The probability of drawing a face card is . A 23.1% chance of drawing a face card.
I hope the above steps were helpful.
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Dr J
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Travel_Word_Problems/230598: An executive flew in the corporate jet to a meeting in a city 1500 miles away. After traveling the same amount of time on the return flight, the pilot mentioned that they still had 300 kilometers to go. The speed of the plane was 600 kilometers per hour. How fast was the wind blowing? (Assume that the wind direction was parallel to the flight path and constant all day.) 1 solutions Answer 170796 by drj(1380) on 2009-10-23 14:18:37 (Show Source):
You can put this solution on YOUR website! An executive flew in the corporate jet to a meeting in a city 1500 miles away. After traveling the same amount of time on the return flight, the pilot mentioned that they still had 300 kilometers to go. The speed of the plane was 600 kilometers per hour. How fast was the wind blowing? (Assume that the wind direction was parallel to the flight path and constant all day.)
Step 1. distance=speed * time
Step 2. Let x be the speed of the wind.
Step 2. Let 600+x be the speed of the plane and the speed of the wind.
Step 3. Let t be the time it takes to go 1500 miles
Step 4. Then, (600 km/hour+x)t=1500 miles since distance traveled is 1500 miles.
Step 5. Convert 1500 miles into kilometers where 1 kilometer = 0.621371192 miles
So in Step 4, it becomes (600+x)t=2424
Step 6. Let 600-x be the speed going in the other direction
Step 7. Then, (600-x)t=2424-300=2124 km since 300 km to go in the same amount of time.
Step 8. Solve for t in Steps 5 and 7 and set the equations equal to each other.
Step 9. Multiply by (600+x)(600-x) to both sides of the equation to get rid of the denominators.
Text form: 2424*(600-x)=2124*(600+x) simplifies to 0=0
Cartoon (animation) form: For tutors: simplify_cartoon( 2424*(600-x)=2124*(600+x) )
If you have a website, here's a link to this solution.
DETAILED EXPLANATION
Look at . Moved to the right of expression It becomes . Look at . Moved to the right of expression It becomes . Look at . Moved these terms to the left It becomes . Look at . Expanded term by using associative property on It becomes . Look at . Multiplied numerator integers It becomes . Look at . Moved to the right of expression It becomes . Look at . Expanded term by using associative property on It becomes . Look at . Multiplied numerator integers It becomes . Look at . Added fractions or integers together It becomes . Look at . Eliminated similar terms, replacing them with It becomes . Look at . Added fractions or integers together It becomes . Look at . Removed extra sign in front of It becomes . Look at . Remove unneeded parentheses around factor It becomes . Look at . Solved linear equation equivalent to -4548*x+180000 =0 It becomes . Result: This is an equation! Solutions: x=39.5778364116095.
Universal Simplifier and Solver
Done!
Step 10. Check times if equal: t=2424/(600+39.6)=3.79 hours, and t=2124/(600-39.6)=3.79 hours.
Step 11. ANSWER: So the wind speed is 39.6 km/hr.
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
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Respectfully,
Dr J
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Travel_Word_Problems/230585: On the first part of a 317 mile trip, a sales person averaged 58 miles per hour. The sales person averaged only 52 miles per hour on the last part of the trip because of an increased volume of traffic. The total time of the trip was 5 hours and 45 minutes. Find the amount of time at each of the two speeds. 1 solutions Answer 170762 by drj(1380) on 2009-10-23 11:22:29 (Show Source):
You can put this solution on YOUR website! On the first part of a 317 mile trip, a sales person averaged 58 miles per hour. The sales person averaged only 52 miles per hour on the last part of the trip because of an increased volume of traffic. The total time of the trip was 5 hours and 45 minutes. Find the amount of time at each of the two speeds.
Step 1. distance = speed * time
Step 2. Let t be the time traveled in the first part of the trip
Step 3. Let 5.75-t be the time traveled in the second part of the trip since 5 hours and 45 minutes is equal to 5.75 and that .
Step 4. Let 58t be the distance traveled at 58 miles per hour.
Step 5. Let 52(5.750-t) be the distance traveled at 52 miles per hour.
Step 6. Then 58t+52(5.75-t)=317 since the total distance of the trip is 317 miles.
Step 7. Solving 58t+52(5.75-t)=317 leads to the following steps
Subtract 299 from both sides of the equation
Divide by 6 to both sides of the equation
and
Check distance traveled if equal to 317
which is a true statement
Step 8. ANSWER: The sales person traveled for 3 hours at 58 miles per hour and for 2 hours and 45 minutes (=2.75 hours) at 52 miles per hour.
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
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Respectfully,
Dr J
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Numbers_Word_Problems/230584: When 2 is added to the difference between 6 times a number and 5, the result is greater than 13 added to 5 times the number find all such numbers? 1 solutions Answer 170758 by drj(1380) on 2009-10-23 11:00:18 (Show Source):
You can put this solution on YOUR website! When 2 is added to the difference between 6 times a number and 5, the result is greater than 13 added to 5 times the number find all such numbers?
Step 1. Let x be the number
Step 2. Let 6x be six times the number.
Step 3. Let 2+6x-5=6x-3 when 2 is added to the difference between 6x a number and 5.
Step 4. Let 6x-3=13+5x since the result is 13 added to 5 times the number.
Step 5. Solving 6x-3=13+5x leads to the following steps
Add 3-5x to both sides of the equation to get only x terms on one side and only numbers on the other side
Step 6. Check solution with Equation in Step 5
which is a true statement
Step 7. ANSWER: The number is 16.
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
And good luck in your studies!
Respectfully,
Dr J
http://www.FreedomUniversity.TV
Miscellaneous_Word_Problems/230586: The difference of two numbers is 16. the larger number is 4 less than 3 times the smaller. Find the two numbers 1 solutions Answer 170755 by drj(1380) on 2009-10-23 10:48:30 (Show Source):
You can put this solution on YOUR website! The difference of two numbers is 16. The larger number is 4 less than 3 times the smaller. Find the two numbers
Step 1. Let x be one and smaller number.
Step 2. Let 3x be three times the smaller number.
Step 3. Let x+16 be the other number since their difference is 16.
Step 4. Then x+16=3x-4 since since the larger number is 4 less than 3 times the smaller.
Step 5. Solving x+16=3x-4 leads to the following steps.
Add 4-x to both sides of the equation to get only x terms on one side and only numbers on the other side.
Divide by 2 to both sides to find x
and
Check if larger number is 4 less than three times the smaller.
which is a true statement
Step 6. ANSWER: The numbers are 10 and 26.
Rectangles/230568: The length of a rectangle is 3 feet longer than the width. The perimeter is 30 feet. find the dimensions of the rectangle
You can put this solution on YOUR website! The length of a rectangle is 3 feet longer than the width. The perimeter is 30 feet. Find the dimensions of the rectangle.
Step 1. Perimeter P means adding up all 4 sides of a rectangle.
Step 2. Let w be the width.
Step 3. Let w+3 be the length since it is 3 feet longer.
Step 4. Then, P=w+w+w+3+w+3 or 4w+6=30
Subtract 6 from both sides of the equation
Divide by 4 to both sides of the equation
and . Note that which is a true statement.
Step 5. ANSWER: The width is 6 feet and the length is 9 feet.
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
Step 3. The diagonal splits the square into two right triangles. As a result, we can use the Pythagorean Theorem which says that the sum of the square of the legs is equal to the hypotenuse. The legs are the sides of the square given as s and let d be the diagonal. Then,
Take the square root to both sides of the equation
Step 4. ANSWER: The diagonal cm or cm
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
Good luck in your studies!
Respectfully,
Dr J
Travel_Word_Problems/230564: Two sports cars leave the city at 9 a.m. One heads due south at 60 mph, the other car travels east at 45 mph. How far apart are they at noon? 1 solutions Answer 170721 by drj(1380) on 2009-10-23 07:59:35 (Show Source):
You can put this solution on YOUR website! Two sports cars leave the city at 9 a.m. One heads due south at 60 mph, the other car travels east at 45 mph. How far apart are they at noon?
Step 1. The two cars travel for 3 hours since the difference between 12 and 9 is 3.
Step 2. distance = speed * time
Step 3. Let 60*3=180 be the distance of the car traveling south.
Step 4. Let 45*3=135 be the distance of the car traveling east.
Step 5. Let d be the distance that the cars are apart after 3 hours.
Step 6. Use the Pythagorean Theorem to find the distance the two cars are apart after 3 hours. The theorem states that the sum of the square of the legs of a right triangle is equal to the square of the hypotenuse ( distance the cars are apart in this example).
Take the square root to both sides of the equation
Step 7. ANSWER: The two cars will be 225 miles apart.
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
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Respectfully,
Dr J
Angles/230562: Two supplementary angles are in the ratio of 11:7. Find the measure of the smaller angle. 1 solutions Answer 170719 by drj(1380) on 2009-10-23 07:48:43 (Show Source):
Step 1. Supplementary angles means two angles add up to 180 degrees.
Step 2. Let x be one angle.
Step 3. Let 180-x be its supplementary angle.
Step 4. since the ratio of two supplementary angles is 11:7.
Step 5. Solving yields the following steps
Multiply 7(180-x) to both sides of the equation
Add 11x to both sides of the equation
Divide by 18 to both sides of the equation
and . Also note the ratio of
Step 6. ANSWER: The smaller angle is 70 degrees.
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
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Respectfully,
Dr J
Miscellaneous_Word_Problems/230561: An apartment building contains 200 apartments. Some apartments have only one bedroom and rent for $435 per month. The rest have two bedrooms and rent for $575 per month. When all the units are rented, the total monthly income is $97,500. How many two-bedroom apartments are there? 1 solutions Answer 170718 by drj(1380) on 2009-10-23 07:37:44 (Show Source):
You can put this solution on YOUR website! An apartment building contains 200 apartments. Some apartments have only one bedroom and rent for $435 per month. The rest have two bedrooms and rent for $575 per month. When all the units are rented, the total monthly income is $97,500. How many two-bedroom apartments are there?
Step 1. Let x be the number of one-bedroom apartments
Step 2. Let 200-x be the number of two-bedroom apartment since there are a total of 200 apartments.
Step 3. Let 435x be the monthly dollar value of one-bedroom apartments.
Step 4. Let 575(200-x) be the monthly dollar value of two-bedroom apartments.
Step 5. Then, be the total monthly dollar value.
Step 6. Solving yields the following steps
Add 140x to both sides of the equation
Subtract 97500 from both sides of the equation
Divide 140 to both sides of the equation
and
Check total monthly value: which is a true statement.
Step 7. ANSWER: The number of two-bedroom apartments is 75.
I hope the above steps were helpful.
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Respectfully,
Dr J
Travel_Word_Problems/230314: The average speed of a moving van is 24 km/h faster than that of a delivery truck. If the van travels the same distance in 5h as the truck travels in 7 h, find the average speed of each. 1 solutions Answer 170575 by drj(1380) on 2009-10-22 18:16:49 (Show Source):
You can put this solution on YOUR website! The average speed of a moving van is 24 km/h faster than that of a delivery truck. If the van travels the same distance in 5h as the truck travels in 7 h, find the average speed of each.
Step 1. Let x be the speed of the delivery truck
Step 2. Let x+24 be the speed of the moving van since it travels 12 km/h faster than the truck.
Step 3. We note that distance=speed*time.
Step 4 Let 7x be the distance traveled by the delivery truck for 7 hours.
Step 5. Let 5(x+24) be the distance traveled by the moving van for 5 hours.
Step 6. Step the expressions in Steps 4 and 5 to be equal since the distance traveled by the truck and van are equal.
Step 7. Solving yields the following steps
Subtract 5x from both sides of the equation
Divide by 2 to both sides of the equation
and .
Check if the distances are the same
which is a true statment.
Step 7. ANSWER: The delivery truck is traveling at 60 km/hr and the moving van is traveling at 84 km/hr.
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
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Dr J
Equations/230291: In 2006 the number of Americans who were members of a health club was 42.7 million. This was an increase of 106% from the number of clubs in 1990. How many Americans were health club members in 1990? 1 solutions Answer 170515 by drj(1380) on 2009-10-22 15:34:55 (Show Source):
You can put this solution on YOUR website! In 2006 the number of Americans who were members of a health club was 42.7 million. This was an increase of 106% from the number of clubs in 1990. How many Americans were health club members in 1990?
Step 1. 106% means 1.06 in decimal form.
Step 2. Let x be the number of Americans who were health club numbers in 1990
Step 3. Let 1.06x be the amount of increase from 1990.
Step 4. Then x+1.06x=42.7 million be the current amount of 42.7.
Step 5. Solving x+1.06x=42.7 yields the following steps
Divide by 2.06 to both sides of the equation
Step 6. ANSWER: The number of club members in 1990 is 20.73 million.
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
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Dr J
Angles/230283: The measure of the supplement of an angle is 60 more than twice the measure of an angle. Find the measure of the larger angle. 1 solutions Answer 170512 by drj(1380) on 2009-10-22 15:27:22 (Show Source):
You can put this solution on YOUR website! The measure of the supplement of an angle is 60 more than twice the measure of an angle. Find the measure of the larger angle.
Step 1. Supplementary angles means two angles add up to 180 degrees.
Step 2. Let x be the angle.
Step 3. Let 2x be twice the angle
Step 4. Let 180-x be the supplementary angle.
Step 5. Then 180-x=2x+60 since the supplement of an angle is 60 more than twice the measure of an angle.
Step 6. Solving 180-x=2x+60 yields the following steps
Add x to both sides of the equation
Subtract 60 from both sides of the equation
Divide by 3 to both sides of the equation
and
Check equation if true...140=2*40+60=140 which is a true statement.
Step 7. The larger angle is 140 degrees.
I hope the above steps were helpful.
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Respectfully,
Dr J
test/230228: The total value of the quarters and dimes in a coin bank is $8.00. If the quarters were dimes and the dimes were quarters, the total value of the coins would be $6.35. Find the number of quarters in the bank.
You can put this solution on YOUR website! The total value of the quarters and dimes in a coin bank is $8.00. If the quarters were dimes and the dimes were quarters, the total value of the coins would be $6.35. Find the number of quarters in the bank.
Step 1. Let x be the number of dimes
Step 2. Let y be the number of quarters since there are 16 coins in all.
Step 3. Let 0.10x be the dollar value of dimes.
Step 4. Let 0.25y be the dollar value of quarters.
Step 5. Then, 0.10x+0.25y=8.00 since the total value of the quarters and dimes in a coin bank is $8.00
Step 6. Then, 0.25x+0.10y=6.35 since if the quarters were dimes and the dimes were quarters, the total value of the coins would be $6.35
Step 7. From Steps 5 and 6, we have the following linear system of equations
Solve: We'll use substitution. After moving 0.25*y to the right, we get: , or . Substitute that
into another equation: and simplify:
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'.
Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
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error_location: 101
Step 8. ANSWER: The number of dimes is 15 and the number of quarters is 26.
I hope the above steps and explanation were helpful.
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Respectfully,
Dr J
http://www.FreedomUniversity.TV
Let x=0, then 0-2y=4 and y=-2. So one point is (0,2)
Let y=0, then x-2*0=4 or x=4. So the other points (-2,4).
We will use these points to graph the line.
Step 3. Let's now work with x=2y.
Let x=0, then 2*0=y or y=0. So one point is (0,0)
Let x=1, then 2*1=y or y=2. So another point is (1,2)
We will use these points to graph the line.
Step 4. The graphs are shown below:
We note that the lines are parallel and have the same slope. The two equations are given in slope-intercept form where y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b) are shown below
For this example we see both lines have a slope and different y-intercepts. One line has a y-intercept of -2 and the other line has a y-intercept of 0.
Step 5. ANSWER: Since the lines are parallel and do not intersect, there are NO SOLUTIONS to this problem.
I hope the above steps were helpful.
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Respectfully,
Dr J
Linear-equations/229979: Two cars, one traveling 12 mph faster-than the other, start at the same time from the same point and travel in opposite directions. In four hours they are 384 mi apart. Find the rate of each car. 1 solutions Answer 170396 by drj(1380) on 2009-10-21 21:05:09 (Show Source):
You can put this solution on YOUR website! Two cars, one traveling 12 mph faster-than the other, start at the same time from the same point and travel in opposite directions. In four hours they are 384 mi apart. Find the rate of each car.
Step 1. Let x be the speed of one car
Step 2. Let x+12 be the speed of the other car since it is traveling 12 mph faster than the other.
Step 3. We note that distance = speed * time.
Step 4. Let 4x be the distance traveling the car in Step 1 after 4 hours.
Step 5. Let 4(x+12) be the speed of the other car in Step 2 after 4 hours.
Step 6. Then, 4x+4x+48=384 since they will be 384 miles apart.
Step 7. Solving the equation in Step 6 yields the following
Subtract 48 from both sides of the equation
Divide by 8 to both sides of the equation
and
4*(42+54)=384 where both cars traveled for 4 hours for a total distance of 384 miles...so it check out.
Step 8. ANSWER: One car traveled at 42 mph and the other car traveled at 54 mph.
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
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Respectfully,
Dr J
http://www.FreedomUniversity.TV
Step 1. Multiply Equation A by 2 to both sides of the equation
Equation A1 Equation B
Step 2. Add Equations A1 and B to get rid of the y-terms
Step 3. Divide by seven to both sides of the equation
Step 4. Substitute into Equation A to get y
Add 2y-3 to both sides of the equation
Divide by 2 to both sides of the equation
Check solution and into Equation B
which is a true statement.
Step 5. ANSWER: The solution is and or (2, -1/2) our intersection point.
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
And good luck in your studies!
Respectfully,
Dr J
http://www.FreedomUniversity.TV
Age_Word_Problems/229963: Miguel is 8 years older than his brother Juan. Five years from now, he will be twice as old as Juan. How old are the boys now? 1 solutions Answer 170381 by drj(1380) on 2009-10-21 20:41:19 (Show Source):
You can put this solution on YOUR website! Miguel is 8 years older than his brother Juan. Five years from now, he will be twice as old as Juan. How old are the boys now?
Step 1. Let x be the age of Juan
Step 2. Let x+8 be the age of Miguel since he is 8 years older than Juan.
Step 3. Let x+5 be the age of Juan five years from now.
Step 4. Let x+8+5=x+13 be the age of Miguel five years from now
Step 5. Then x+13=2(x+5) since five years from now Miguel will be twice as old as Juan.
Step 6. Solving x+13=2(x+5) yields the following steps
Subtract 10 from both sides of the equation
Subtract x from both sides of the equation
and .
Now five years from now Miguel will be 16 and Juan will be 8 which is twice as old as Juan and this is a true statement.
Step 7. ANSWER: Juan is 3 years old and Miguel is 11 years old.
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
And good luck in your studies!
Respectfully,
Dr J
http://www.FreedomUniversity.TV
Graphs/229955: I need to know how to graph the equation y=3x+7 1 solutions Answer 170375 by drj(1380) on 2009-10-21 20:34:10 (Show Source):
Step 2. Let x=0, then y=3*0+7=7. So one point is (0,7).
Step 3. Let x=-2, then y=3(-2)+7=1. So another point is (-2,1).
Step 4. Use these two points (0,7) and (-2,1) to draw a line as shown below.
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
And good luck in your studies!
Respectfully,
Dr J
http://www.FreedomUniversity.TV
Travel_Word_Problems/229958: A plane is flying due east in still air at 395 km/h. How far will the plane travel in 3 hours?
Step 3. ANSWER: Distance traveled by the plane is 1185 km.
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
And good luck in your studies!
Respectfully,
Dr J
http://www.FreedomUniversity.TV
Linear-equations/229937: Given the following system of linear equation, make comment about the lines and the number of solutions this system has.
y = -3x - 12
y = 2x + 12 1 solutions Answer 170361 by drj(1380) on 2009-10-21 19:59:21 (Show Source):
You can put this solution on YOUR website! Given the following system of linear equation, make comment about the lines and the number of solutions this system has.
y = -3x - 12 Equation A
y = 2x + 12 Equation B
Step 1. The above lines in given in slope intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b).
Step 2. The slope of Equation A is m1=-3 and the slope of Equation B is m2=2. So they are not parallel since the parallel lines have the same slope. The lines are not perpendicular since the product of their slopes is not equal to -1 since m1*m2 does not equal -1.
Step 3. The lines intersect at a point so there is one solution.
Here's a graph of the two lines
The intersection between these two lines is given below using substituion:
Solve: We'll use substitution. After moving 1*y to the right, we get: , or . Substitute that
into another equation: and simplify:
Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
'.
Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101
Same results as before.
I hope the above steps and explanation were helpful.
For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry.
Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.
Step 1. It takes two points to make a line. Let's find these two points
Step 2. Let x=0, then 3*0-2*y=-6 or y=3. So we have (0,3) as one point.
Step 3. Let y=0, then 3x-2*0=-6 or x=-2. So we have (-2,0) as another point.
Step 4. Use these two points (0,3) and (-2,0) to draw the line.
METHOD 2
Step 1. Let's put the equation in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point(0,b).
Step 2. Putting in slope-intercept form yields the following steps.
Add 2y+6 to both sides of the equation
Divide 2 to both sides of the equation
}
Step 3. ANSWER: The equation is where the slope m=3/2 and y-intercept b=3.
Need one more point to graph the line since we have (0,3) as one point. A slope m=3/2 means every move to two units to the right yields three steps upward.
So starting at (0,3) then one unit to the right means x2=0+2=2 and then two units down means y2=3+3=6. Then, the other point we can use to plot the line is (2,6). We can check if it satisfies the equation or
which it does.
Here's the graph:
I hope the above steps and explanation were helpful.
For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry.
Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.
Respectfully,
Dr J
http://www.FreedomUniversity.TV
Linear-equations/229924: find the equation of the line containing the given pair of points (-9,0)(0,7) 1 solutions Answer 170351 by drj(1380) on 2009-10-21 19:38:44 (Show Source):
Step 1. We will put the equation of the line in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b).
Step 2. The slope of the line m is given as
where for our example is x1=-9, y1=0, x2=0 and y2=7 (think of ). You can choose the points the other way around but be consistent with the x and y coordinates. You will get the same result.
Step 3. Substituting the above values in the slope equation gives
Step 4. The slope is calculated as or
Step 5. Now use the slope equation of Step 2 and choose one of the given points. I'll choose point (0,7). Letting y=y2 and x=x2 and substituting in the slope equation given as,
Step 6. Multiply both sides of equation by x to get rid of denomination found on the right side of the equation
Step 7. Now simplify and put the above equation into slope-intercept form.
Add 7 to both sides of the equation
This is in slope-intercept form where the slope m=7/9 and y-intercept b=0
Step 8. See if the other point (-9,0) or x=-9 and y=0 satisfies this equation
So the point (-9,0) satisfies the equation and is on the line. In other words, you can use the other point to check your work.
Step 9. ANSWER: The equation of the line is
Note: above equation can be also be transform into standard form as
See graph below to check the above steps.
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
Good luck in your studies!
Respectfully,
Dr J
Age_Word_Problems/229585: Matt is 22 yars older than belinda. 7 years ago Matt was 3 times as old as belinda, find the age of each now. please help, I have so far
7 yrs ago
Matt: M M-7
Belinda: M-22 M-29
(m-7) + (m-29) = 36 1 solutions Answer 170195 by drj(1380) on 2009-10-21 10:51:33 (Show Source):
You can put this solution on YOUR website! Matt is 22 yars older than Belinda. 7 years ago Matt was 3 times as old as belinda, find the age of each now. please help, I have so far
7 yrs ago
Matt: M M-7
Belinda: M-22 M-29
(m-7) + (m-29) = 36
Nice effort...Here's how I'd set up and solve the problem...
Step 1. Let m be the current age of Belinda
Step 2. Let m+22 be the age of Matt.
Step 3. Let m-7 be the age of Belinda seven years ago.
Step 4. Let m+22-7=m+15 be the age of Matt seven years ago.
Step 5. Then since 7 years ago Matt was 3 times as old as Belinda.
Step 6. Solving yields the following steps
Add 21 to both sides of the equation
Subtract m from both sides of the equation
Divide by 2 to both sides of the equation
and
Check with original statement: Seven years ago Belinda is 11 and Matt is 33 when Matt was 3 times as old as Belinda.
Step 7. ANSWER: Belinda is 18 years old and Matt is 40 years old.
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
Good luck in your studies!
Respectfully,
Dr J
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
Age_Word_Problems/229587: Please help me with this problem. I really need this ASAP.
Mary is 12 years older than her sister, Martha. The product of their ages is 540. How old is each? 1 solutions Answer 170191 by drj(1380) on 2009-10-21 10:36:57 (Show Source):
You can put this solution on YOUR website! Mary is 12 years older than her sister, Martha. The product of their ages is 540. How old is each?
Step 1. Let x be the age of Martha.
Step 2. Let x+12 be the age of Mary.
Step 3. Then since the product of their ages is 540.
Step 4. We can form a quadratic equation by subtracting 540 from both sides of the equation
Step 4. To solve, use the quadratic formula given as
Quadratic equation (in our case ) has the following solutons:
For these solutions to exist, the discriminant should not be a negative number.
First, we need to compute the discriminant : .
Discriminant d=2304 is greater than zero. That means that there are two solutions: .
Quadratic expression can be factored:
Again, the answer is: 18, -30.
Here's your graph:
Step 5. Selecting the positive answer x=18 then x+12=30 and note the product of 18 and 30 is 540.
Step 6. ANSWER: Martha is 18 years old and Mary is 30 years old.
I hope the above steps were helpful.
For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
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