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Money_Word_Problems/640123: if i had one dollar and i brought 100 pieces of candy, some at 5 cent each and some at 2 cent each and some at 10 for 1 cents , so how many pieces of candy did i purchase at each cent. 1 solutions Answer 403074 by ankor@dixie-net.com(15747)   on 2012-08-22 21:41:24 (Show Source): You can put this solution on YOUR website! If I had one dollar and I brought 100 pieces of candy; some at 5 cent each, and some at 2 cent each, and some at 10 for 1 cents, How many pieces of candy did I purchase at each cent. : Let x = no. of 5 cent candies Let y = no. of 2 cent candies Let z = no. of 10 for 1 cent : x + y + z = 100 candies : 5x + 2y + .1z = 100 cents We have 3 unknowns and two equations, but we know 10 for one cent, candies has to be a multiple of 10, and <100 : Let z = 70 candies x + y + 70 = 100 x + y = 30; subtracted 70 from both sides then 5x + 2y + .1(70) = 100 5x + 2y + 7 = 100 5x + 2y = 93; subtracted 7 from both sides : Multiply the 1st equation by 2, subtract from the above equation 5x + 2y = 93 2x + 2y = 60 -------------- subtraction eliminates y, find x 3x = 33 x = 11 ea 5 cent candies : Find y x + y + z = 100 11 + y + 70 = 100 y = 100 - 81 y = 19 ea 2 cent candies : : See if that works 5(11) + 2(19) + .1(70) = 55 + 38 + 7 = 100 cents : Summarize 11 ea 5 cent candies 19 ea 2 cent candies 70 ea 10/1 cent candies

Unit_Conversion_Word_Problems/640061: The world record for the hundred meter dash is 9.77 seconds. What is the corresponding average speed in units of miles per second, kilometers per hour, feet per second, and miles per hour? At this speed, how long will it take to run 1.00? 1 solutions Answer 403031 by ankor@dixie-net.com(15747)   on 2012-08-22 18:40:41 (Show Source): You can put this solution on YOUR website! The world record for the hundred meter dash is 9.77 seconds. What is the corresponding average speed in units of miles per second, kilometers per hour, feet per second, and miles per hour? : Find meters/sec: = 10.2354 m/sec : Find km/hr: = 36.84675 km/hr : Convert to mph: 36.84675 * .6214 = 22.897 mph : Convert to ft/sec: 10.2354 * 3.28 = 33.572 ft/sec : At this speed, how long will it take to run 1.00? One what? Assume you mean 1 mile = 157.274 seconds (2 min 37.274) sec to go 1 mile

Word_Problems_With_Coins/640002: How do I solve: a man has 10 dallors to buy stamps. He wants to buy twice as many 22 cent stamps as 14 cent stamps. What is the greatest number of 22 cent stamps he can buy? 1 solutions Answer 403017 by ankor@dixie-net.com(15747)   on 2012-08-22 17:27:16 (Show Source): You can put this solution on YOUR website! A man has 10 dollars to buy stamps. He wants to buy twice as many 22 cent stamps as 14 cent stamps. What is the greatest number of 22 cent stamps he can buy? : let x = no. of 22 cent stamps let y = no. of 14 cent : Write an equation for each statement. : "A man has 10 dallors to buy stamps." .22x + .14y = 10.00 : "He wants to buy twice as many 22 cent stamps as 14 cent stamps." x = 2y We want to find x, divide both sides by 2 y = .5x : Replace x with 2y in the 1st equation .22x + .14(.5x) = 10.00 .22x + .07x = 10.00 .29x = 10.00 x = 10/.29 x = 34 ea 22 cent stamps is the most he can buy & still get at least 17 ea 14 cent stamps What is the greatest number of 22 cent stamps he can buy?

Travel_Word_Problems/640045: A bus took a 700 mile trip in 12 hours. The speed was 75 mph for the first part of the trip, and 50 mph for the return trip. How many hours were traveled at each speed? 1 solutions Answer 403013 by ankor@dixie-net.com(15747)   on 2012-08-22 17:13:59 (Show Source): You can put this solution on YOUR website! A bus took a 700 mile trip in 12 hours. The speed was 75 mph for the first part of the trip, and 50 mph for the return trip. How many hours were traveled at each speed? : Let t = time in hrs at 75 mph The total travel time is given as 12 hrs, therefore (12-t) = time at 55 mph : Write a distance equation; dist = speed * time 75t + 50(12-t) = 700 75t + 600 - 50t = 700 75t - 50t = 700 - 600 25t = 100 t = 100/25 t = 4 hrs at 75 mph then 12-4 = 8 hrs at 50 mph : : Check this by finding the distance at each speed 4(75) = 300 mi 8(50) = 400 mi -------------- total: 700 mi

Travel_Word_Problems/640041: A plane leaves New York for Los Angeles traveling at an average speed of 500 miles per hour. A second plane leaves from Los Angeles two hours later bound for New York, 3200 miles away. Taking advantage of the jetstream, the second plane averages 600 mph. How many hours after the first plane took off will the two planes pass each other? 1 solutions Answer 403007 by ankor@dixie-net.com(15747)   on 2012-08-22 16:21:19 (Show Source): You can put this solution on YOUR website! A plane leaves New York for Los Angeles traveling at an average speed of 500 miles per hour. A second plane leaves from Los Angeles two hours later bound for New York, 3200 miles away. Taking advantage of the jetstream, the second plane averages 600 mph. How many hours after the first plane took off will the two planes pass each other? : Let t = travel time of the 1st plane then (t-2) = travel time of the 2nd plane : When the two planes meet, they will have traveled a total of 3200 miles Write a distance equation; dist = speed * time : 500t + 600(t-2) = 3200 500t + 600t - 1200 = 3200 1100t = 3200 + 1200 1100t = 4400 t = 4400/1100 t = 4 hrs after the 1st plane takes off they will meet : : Check by finding the actual distance each plane traveled 4(500) = 2000 2(600) = 1200 -------------- total d: 3200

test/639930: Solve the simultaneous equation :f-2g+3=2f-3g+2=1 1 solutions Answer 403003 by ankor@dixie-net.com(15747)   on 2012-08-22 16:09:31 (Show Source): You can put this solution on YOUR website! Solve the simultaneous equation : Assume the equations are: (some commas, and/or spaces would help) f - 2g + 3 = 2 f - 3g + 2 = 1 combine the numerical terms on the right f - 2g = 2 - 3 f - 2g = -1 and f - 3g = 1 - 2 f - 3g = -1 : Using elimination f - 2g = -1 f - 3g = -1 -------------- Subtraction eliminates f, find g g = 0 then obviously f = -1

Equations/639672: I don't know if this is Algebra but I need help. What is the answer to x-(4x-7)=5x-(x+21) 1 solutions Answer 402977 by ankor@dixie-net.com(15747)   on 2012-08-22 14:22:13 (Show Source): You can put this solution on YOUR website! What is the answer to x - (4x-7) = 5x - (x+21) removing brackets will change the signs, same as mult the inside terms by -1 x - 4x + 7 = 5x - x - 21 -3x + 7 = 4x - 21 7 + 21 = 4x + 3x 28 = 7x x = 28/7 x = 4 : : Check solution in the original problem, replace x with 4 4 - (4(4)-7) = 5(4) -(4+21)

Quadratic-relations-and-conic-sections/639442: A necklace hanging between two fixed points A and B at the same level. The length of the necklace between the two points is 100cm. The midpoint of the necklace is 8cm below A and B. Assume that the necklace hangs in the form of parabolic curve, find the equation of the curve. 1 solutions Answer 402849 by ankor@dixie-net.com(15747)   on 2012-08-21 19:42:19 (Show Source): You can put this solution on YOUR website! A necklace hanging between two fixed points A and B at the same level. The length of the necklace between the two points is 100cm. The midpoint of the necklace is 8cm below A and B. Assume that the necklace hangs in the form of parabolic curve, find the equation of the curve. : Two coordinates; x = 50, y = -8 50^2a + 50b = -8 2500a + 50b = -8 and x = 100, y = 0 100^2a + 100b = 0 10000a + 100b = 0 : Multiply the 1st equation by 2, subtract from the 2nd equation 10000a + 100b = 0 5000a + 100b = -16 ---------------------subtraction eliminates b find a 5000a = 16 a = 16/5000 a = .0032 : Find b 2500(.0032) + 50b = -8 8 + 50b = -8 50b = -8 - 8 b = -16/50 b = -.32 : The equation: y = .0032x^2 - .32x Which looks like

test/639561: Im in 8th grade pre ap algebra and needing help on homework 1 solutions Answer 402795 by ankor@dixie-net.com(15747)   on 2012-08-21 15:49:46 (Show Source): You can put this solution on YOUR website! On this site you need to submit a specific problem, (as accurately as possible) You can request step-by-step instructions to solve it.

Rational-functions/639422: please help me solve. The students in my class are wearing 6 more green shirts than yellow shirts. The ratio of green shirts to yellow shirts is 5:3. Find the total number of shirts 1 solutions Answer 402794 by ankor@dixie-net.com(15747)   on 2012-08-21 15:47:32 (Show Source): You can put this solution on YOUR website! The students in my class are wearing 6 more green shirts than yellow shirts. The ratio of green shirts to yellow shirts is 5:3. Find the total number of shirts. : Find this using a multiplier, let x = the multiplier then 5x = no. of green shirts 3x = no. of yellow and 8x = total number of shirts : "wearing 6 more green shirts than yellow shirts." 5x = 3x + 6 we know = replace 5x with (3x+6) = Cross multiply 5(3x) = 3(3x+6) 15x = 9x + 18 15x - 9x = 18 6x = 18 x = 18/6 x = 3 is the multiplier therefore 8(3) = 24 total number of shirts c

Geometry_Word_Problems/639417: A square's side is increased by 4 yards, which corresponds to an increase in the area by 80 square yards. How many yards is the side of the initial square? 1 solutions Answer 402791 by ankor@dixie-net.com(15747)   on 2012-08-21 15:34:06 (Show Source): You can put this solution on YOUR website! A square's side is increased by 4 yards, which corresponds to an increase in the area by 80 square yards. How many yards is the side of the initial square? : Let x = the side of the initial square then x^2 = the initial area of the square and (x+4)^2 = the area of the new square : New area - initial area = 80 sq/yds (x+4)^2 - x^2 = 80 FOIL(x+4)(x+4) x^2 + 8x + 16 - x^2 = 80 x^2 - x^2 + 8x = 80 - 16 8x = 64 x = x = 8 yds the side of the initial square : : Check this; new square side; 4 + 8: 12^2 - 8^2 = 144 - 64 = 80

Travel_Word_Problems/639400: A distance of 360km is covered in 3 hours how fast is the car driving 1 solutions Answer 402782 by ankor@dixie-net.com(15747)   on 2012-08-21 14:38:33 (Show Source): You can put this solution on YOUR website! A distance of 360km is covered in 3 hours. how fast is the car driving: : remember that speed = dist/time s =

test/639410: Andy opened a book and the product of the two page numbers facing him was 552. Find the sum of the two page numbers. 1 solutions Answer 402779 by ankor@dixie-net.com(15747)   on 2012-08-21 14:20:48 (Show Source): You can put this solution on YOUR website! Andy opened a book and the product of the two page numbers facing him was 552. Find the sum of the two page numbers. : Let x = one page then (x+1) = the other page : The product x(x+1) = 552 x^2 + x - 552 = 0 Factors to (x+24)(x-23) = 0 the positive solution x = 23 is the page on the left and 24 is page on the right

Miscellaneous_Word_Problems/639286: PLEASE HELP! ASAP Mrs. Howell, your science teacher, overheard two of her students talking about how to convert temperatures from celsius to farenheit and vice versa. The students said they knew there was a formula, but they did not remember what it was it was. Mrs. Howell remarked to you that if they just knew about the freezing point and boiling point of water for each temperature scale, the formula could be easily be "rediscovered." Mrs. Howell has asked you to write a explanation for how to find the formula, showing all of your calculations. Mrs. Howell also wants you to include an explanation of each of the parts of the formula. ( Don't forget to include the formula for celsius to farenheit and the formula for farenheit to celsius.) 1 solutions Answer 402701 by ankor@dixie-net.com(15747)   on 2012-08-20 22:04:19 (Show Source): You can put this solution on YOUR website! Mrs. Howell remarked to you that if they just knew about the freezing point and boiling point of water for each temperature scale, the formula could be easily be "rediscovered." Mrs. Howell has asked you to write a explanation for how to find the formula, showing all of your calculations. Mrs. Howell also wants you to include an explanation of each of the parts of the formula. ( Don't forget to include the formula for Celsius to Fahrenheit and the formula for Fahrenheit to Celsius.) : we know Celsius: Water freezes: 0 degrees, Water boils (at sea level): 100 s Fahrenheit: Water freezes: 32 degrees, Water boils: 212 degrees : let x = Fahrenheit degrees let y = Celsius degrees : Using the slope/intercept equation y = mx + b : Find the slope, assign the values as follows x1 = 32; y1 = 0 x2 =212; y2 = 100 m = m = = = is the slope : Use the point/slope form to find the equation: y - y1 = m(x-x1) y -0 = (x - 32) y = (x-32) or the familiar formula to convert Fahrenheit to Celsius c = (f - 32) : To convert Celsius to Fahrenheit, solve for f (f - 32) = c Multiply both sides by 9/5, results: f - 32 = c add 32 to both sides f = c + 32;

Proportions/639151: The ratio of salt to water in a certain solution is 4 to 15. if the solution contains 6 ounces of water, how many ounces of salt does it contain? 1 solutions Answer 402651 by ankor@dixie-net.com(15747)   on 2012-08-20 18:47:16 (Show Source): You can put this solution on YOUR website! The ratio of salt to water in a certain solution is 4 to 15. if the solution contains 6 ounces of water, how many ounces of salt does it contain? : Let s = amt of salt + Cross multiply 15s = 6 * 4 15s = 24 s = 24/15 s = 1.6 oz of salt

Money_Word_Problems/639174: Hey Im stumped on an alg 2 story problem; A salesperson at a car dealership has a base salary of $25,000 per year and earns a 5% commission on total sales. How much must the salesperson sell to earn $50,000 in one year? I don't understand what the 5% is "of." like 12 is 50% OF 24. But there is no number to base that 5% off of. 1 solutions Answer 402650 by ankor@dixie-net.com(15747)   on 2012-08-20 18:36:30 (Show Source): You can put this solution on YOUR website! A salesperson at a car dealership has a base salary of $25,000 per year and earns a 5% commission on total sales. How much must the salesperson sell to earn $50,000 in one year? : Let a = amt that he has to sell to make 50k : Commis + base = 50k .05a + 25000 = 50000 .05a = 50000 - 25000 .05a = 25000 a = 25000/.05 a = $500,000 he has to sell to make a total of 50k

Human-and-algebraic-language/639162: Please show me how to solve this problem Richard's average driving speed is 3 miles per hour faster than grace's. In the same length oftime it takes Richard to drive 180miles, Grace only drives 168 miles. What is Richard's average driving speed? 1 solutions Answer 402618 by ankor@dixie-net.com(15747)   on 2012-08-20 17:08:37 (Show Source): You can put this solution on YOUR website! Richard's average driving speed is 3 miles per hour faster than grace's. In the same length it takes Richard to drive 180 miles, Grace only drives 168 miles. What is Richard's average driving speed? : let s = Grace's driving speed then (s+3) = Richard's speed : Write a time equation; time = dist/speed : R's travel time = G's travel time = Cross multiply, solve for s

Expressions-with-variables/638983: I need help with substitution. x+3=y 3x+4y=7 with steps & answers please and thank you 1 solutions Answer 402588 by ankor@dixie-net.com(15747)   on 2012-08-20 15:06:56 (Show Source): You can put this solution on YOUR website! substitution. x + 3 = y 3x + 4y = 7 : From the 1st equation we know that: y = (x+3) Substitute (x+3) for y in the 2nd equation 3x + 4(x+3) = 7 : multiply what's inside the brackets 3x + 4x + 12 = 7 : Add the x's, subtract 12 from both sides 7x = 7 - 12 7x = -5 x = : Find y y = x + 3 substitute for x y = + 3 Change 3 to 7ths y = + y = : Solution: x = ; y = : : Check solution in the 2nd equation 3x + 4y = 7 Replace x and y 3() + 4() = 7 + = 7 = 7 7 = 7; confirms our solutions, : Was this step-by-step enough for you to understand? C

Trigonometry-basics/638985: A tank at a marine exhibit contains 2000 gallons of sea water. The sea water is 7.5% salt. How many gallons, to the nearest gallon, of fresh water must be added to the tank so that the mixture contains only 7% salt? 1 solutions Answer 402584 by ankor@dixie-net.com(15747)   on 2012-08-20 14:40:31 (Show Source): You can put this solution on YOUR website! A tank at a marine exhibit contains 2000 gallons of sea water. The sea water is 7.5% salt. How many gallons, to the nearest gallon, of fresh water must be added to the tank so that the mixture contains only 7% salt? : Let x = amt of fresh water required to accomplish this : remember, the amt of salt stays the same only the per cent changes : .075(2000) = .07(x+2000) 150 = .07x + 140 150 - 140 = .07x 10 = .07x x = 10/.07 x = 142.857 ~ 143 gallons of fresh water required.

Linear_Equations_And_Systems_Word_Problems/639043: The ages of A and B are in ration of 7:5, 10 year hence the ratof their ages will be 9:7, find their present ages 1 solutions Answer 402570 by ankor@dixie-net.com(15747)   on 2012-08-20 13:32:54 (Show Source): You can put this solution on YOUR website! The ages of A and B are in ratio of 7:5, 10 year hence the ratio of their ages will be 9:7, find their present ages : The easy way to do this is by using a "multiplier" let x = the multiplier then 7x = A's present age and 5x = B's present age : Adding 10 yrs to their age produces a ratio of 9:7, there = cross multiply 7(7x+10) = 9(5x+10) 49x + 70 = 45x + 90 49x - 45x = 90 - 70 4x = 20 x = 20/4 x = 5 is the multiplier : Their present ages A: 5(7) = 35 yrs B: 5(5) = 25 yrs : : You can check this for yourself, add 10 yrs to their ages and find the ratio

Miscellaneous_Word_Problems/638910: The half-life of a certain radioactive material is 32 days. An initial amount of the material has a mass of 361 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 5 days. Round your answer to the nearest thousandth. 1 solutions Answer 402491 by ankor@dixie-net.com(15747)   on 2012-08-19 22:02:50 (Show Source): You can put this solution on YOUR website! The half-life of a certain radioactive material is 32 days. An initial amount of the material has a mass of 361 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 5 days. Round your answer to the nearest thousandth. : The radio active decay formula: A = Ao*2^(-t/h); where A = remaining amt after t time Ao = initial amt t = time of decay h = half-life of the substance : A = 391*2^(-5/32) using a calc find 2^(-5/32) A = 391 * .89735 A = 350.866 kg

Travel_Word_Problems/638885: a plane flies at a height of 1800 feet over a 150-foot-tall building. how far above the building is the plane? draw a diagram to explain your answer. I just need help on how to draw a diagram or what kind of diagram 1 solutions Answer 402485 by ankor@dixie-net.com(15747)   on 2012-08-19 21:36:03 (Show Source): You can put this solution on YOUR website! a plane flies at a height of 1800 feet over a 150-foot-tall building. how far above the building is the plane? draw a diagram to explain your answer. : ---plane (1800') : : : : : : ---Building (150') : __Ground (0') ; The plane is: 1800 - 150 = 1650' above the building

Finance/638835: What exactly does algebra include? 1 solutions Answer 402484 by ankor@dixie-net.com(15747)   on 2012-08-19 21:29:13 (Show Source): You can put this solution on YOUR website! This is not "exactly" but a general description of algebra : "Algebra is the study of properties of operations carried out on sets of numbers. Algebra is a generalization of arithmetic in which symbols, usually letters, are used to stand for numbers. The structure of algebra is based upon axioms which are statements that are assumed to be true."

Travel_Word_Problems/638920: Please help me solve this word problem. When Chiko 'volunteers' for the army, he says that the ride on the bus lasted 'endless' hours. If the truck he was in was moving at a rate of 30 km/hr and the bus ride lasted for 13 hours, how far did the soldiers take him from home? How far in miles? I think I divide 13 into 30 which equals 0.43333 but that doesn't make sense.. please e-mail me back at twogunsdown@ymail.com... thank you. Rehyna 1 solutions Answer 402481 by ankor@dixie-net.com(15747)   on 2012-08-19 21:11:49 (Show Source): You can put this solution on YOUR website! If the truck he was in was moving at a rate of 30 km/hr and the bus ride lasted for 13 hours, how far did the soldiers take him from home? How far in miles? : Remember; dist = speed * time : 13 * 30 = 390 km

Equations/638899: The question is: You are building a walkway of uniform width around a 100ft by 60ft swimming pool. After completing the walkway, you want to put a fence along the outer edge of the walkway. You have 450ft of fencing to enclose the walkway. What is the maximum width of the walkway? I think that the walkway is 75ft by 150ft. I'm not sure though and I am very confused on what I should do to get the answer. I have tried several things and nothing is working right. Please help. 1 solutions Answer 402480 by ankor@dixie-net.com(15747)   on 2012-08-19 21:07:34 (Show Source): You can put this solution on YOUR website! You are building a walkway of uniform width around a 100ft by 60ft swimming pool. After completing the walkway, you want to put a fence along the outer edge of the walkway. You have 450ft of fencing to enclose the walkway. What is the maximum width of the walkway? : Actually they are asking for width of the walkway. : let x = the width of the walkway that will add 2x to each dimension of the pool : the overall dimensions including the walkway will be (2x+100) by (2x+60) : The fencing will equal the perimeter of the area including the walkway 2L + 2W = 450 Using the overall dimensions for L and W: 2(2x+100) + 2(2x+60) = 450 simplify divide thru by 2 (2x+100) + (2x+60) = 225 combine like terms 4x + 160 = 225 4x = 225 - 160 4x = 65 x = 65/4 x = 16.25 ft is the width of the walkway if you use 450 ft of fence : : you can check this by finding the overall dimensions (32.5+100) by (32.5+60) 132.5 by 92.5 : See if this equal the amt of fencing 2(132.5) + 2(92.5) = 265 + 185 = 450

Functions/638711: please help me solve this equation this is factor completely 1 solutions Answer 402411 by ankor@dixie-net.com(15747)   on 2012-08-19 16:18:48 (Show Source): You can put this solution on YOUR website! Factor: 5a + 10b - ax - 2bx ; Group factor, factor out 5, then factor out -x 5(a + 2b)- x(a + 2b); (the minus changes the signs) : Factor out (a+2b) (a + 2b)(5 - x)

Travel_Word_Problems/638504: Kate runs twice as fast as she walks. On her way to school, she walks for twice the length of time as she runs. In this way she takes 20 minutes to get there. On her way home, she runs for twice the length of time as she walks. How long does she take to get home? 1 solutions Answer 402407 by ankor@dixie-net.com(15747)   on 2012-08-19 16:04:17 (Show Source): You can put this solution on YOUR website! Kate runs twice as fast as she walks. On her way to school, she walks for twice the length of time as she runs.Le In this way she takes 20 minutes to get there. On her way home, she runs for twice the length of time as she walks. How long does she take to get home? : Let s = the walking speed and 2s = the running speed : From the information given, we know she walked (20)min and ran (20)min Using decimals, walked 13.33 min and ran 6.67 min Find the distance; dist = time * speed 13.33s + 6.67(2s) = 26.67s is the distance one way : "On her way home, she runs for twice the length of time as she walks." let t = time she walked going home then 2t = time she ran going home Another distance equation st + 2s(2t) = 26.67s st + 4st = 26.67s Divide thru by s t + 4t = 26.67 5t = 26.67 t = t = 5 spent walking and 10 spend running then total time to return 5 + 10 = 16 min to return home

Miscellaneous_Word_Problems/638374: A wire of length 16 inches is to be cut into two pieces; then each piece will be bent to form a square. Find the length of the two pieces assuming that the sum of the areas of the two squares is 10 square inches. 1 solutions Answer 402279 by ankor@dixie-net.com(15747)   on 2012-08-18 17:16:18 (Show Source): You can put this solution on YOUR website! A wire of length 16 inches is to be cut into two pieces; then each piece will be bent to form a square. Find the length of the two pieces assuming that the sum of the areas of the two squares is 10 square inches. : Let the length of the sides of the two square be x & y : 4x + 4y = 16 simplify, divide by 4 x + y = 4 y = (4-x) and x^2 + y^2 = 10 : Replace y with (4-x) x^2 + (4-x)^2 = 10 FOIL (4-x)(4-x) x^2 + 16 - 8x + x^2 = 10 Combine like terms on the left x^2 + x^2 - 8x + 16 - 10 = 0 2x^2 - 8x + 6 = 0 simplify, divide by 2 x^2 - 4x + 3 = 0 Factors to (x-1)(x-3) = 0 Two solutions x = 1, then y = 3 and x = 3, then y = 1 : : You can check if this is true in the two original equations

Travel_Word_Problems/638031: The distance between city A and B is 28 km. Two hikers left from each city (One from city A to city B and the other from city B to city A) heading towards each other at the same speed. The hiker from city A rested for an hour after having walked 9 km and then continued at a speed greater than 1 km/hour than his previous speed, then rested again 4 km away from city B. There he met the hiker from city B, who walked at a constant speed without resting until the two met. What were the speeds of the two hikers? 1 solutions Answer 402276 by ankor@dixie-net.com(15747)   on 2012-08-18 16:56:50 (Show Source): You can put this solution on YOUR website! The distance between city A and B is 28 km. Two hikers left from each city (One from city A to city B and the other from city B to city A) heading towards each other at the same speed. The hiker from city A rested for an hour after having walked 9 km and then continued at a speed greater than 1 km/hour than his previous speed, then rested again 4 km away from city B. There he met the hiker from city B, who walked at a constant speed without resting until the two met. What were the speeds of the two hikers? : Let s = speed of the two hikers then (s+1) = speed of the A after his 1 hr rest : Find the distance hiker A traveled after his rest, to meet B, 4 km from City B 28-9-4 = 15 km : Write a time equation; time = dist/speed + + 1 = : + = - 1 : = : = : = Multiply both sides by s = (4 - s) 24s + 9 = (s+1)(4-s) FOIL the right side 24s + 9 = 4s - s^2 + 4 - s 24s + 9 = 3s - s^2 + 4 Combine on the left s^2 + 24s - 3s + 9 - 4 = 0 s^2 + 21s + 5 = 0 Actually this equation has two negative solutions so the given scenario is not possible. It seems unreasonable, to find a speed, where A travels 24 km (+ a rest), while B travels 4 km

Travel_Word_Problems/638020: At the same time, two hikers took off, one from city B to city A and the other from city A to city B. They hiked the same distance and their speeds were constant. They met on the way, and it was revealed that the hiker from city B to city A traveled two km more than the other hiker. This hiker arrived to city A 40 minutes after the two met, and the hiker from city A arrived to city B an hour and a half after they met. What is the distance of the trail? 1 solutions Answer 402254 by ankor@dixie-net.com(15747)   on 2012-08-18 13:25:18 (Show Source): You can put this solution on YOUR website! At the same time, two hikers took off, one from city B to city A and the other from city A to city B. They hiked the same distance and their speeds were constant. They met on the way, and it was revealed that the hiker from city B to city A traveled two km more than the other hiker. This hiker arrived to city A 40 minutes after the two met, and the hiker from city A arrived to city B an hour and a half after they met. What is the distance : Do this using minutes for the time let t = travel time to the point where they met : let x = dist from A to the meeting point and (x+2) = dist from B to the meeting point then x + (x+2) = 2x+2 km is the distance from A to B : A<-----40min------*---------t min-------< B(hiker B's path) A------x km-------*-------(x+2)km-------B A>-----t Min------*--------90min--------> B (hiker A's path) : Hiker B, = Cross multiply tx = 40(x+2) tx = 40x + 80 t = : Hiker A = Cross multiply t(x+2) = 90x t = : t=t, therefore: = Cross multiply 90x^2 = (x+2)(40x+80) FOIL 90x^2 = 40x^2 + 80x + 80x + 160 90x^2 = 40x^2 + 160x + 160 Combine on the left 90x^2 - 40x^2 - 160x - 160 = 0 50x^2 - 160x - 160 = 0 Simplify, divide by 10 5x^2 - 16x - 16 = 0 Factors to (5x + 4)(x - 4) = The positive solution is all we want here x = 4 "What is the distance?" 2(4) + 2 = 10 km is the distance from A to B : : Confirm this, find t t = t = 60 min Find the speed of A & B A's time in hrs (90+60)/60 = 2.5 hrs A's speed 10/2.5 = 4 km/hr and B's time in hrs (40+60)/60 = 1 hrs A's speed 10/1.67 ~ 6 km/hr : Find how far each traveled in 1 hr (t) B: 6 km A: 4 km --------- dif: 2 km

Linear_Equations_And_Systems_Word_Problems/638354: A professor announces that course grades will be computed by taking 40% of a student's project score (0-100 points) and adding 60% of the students final exam score (0-100 points). If a student gets an 86 on the project, what scores can she get on the final exam to get a course grade of at least 90? These are some conclusions I've made, which may or may not be correct. 40%(86)+60%(x) is greater than or equal to 90. I am confused by the word "And" in the problem. Does this let me know that this is a compound inequality? If so, what other numbers do I use to create another inequality...100? 1 solutions Answer 402160 by ankor@dixie-net.com(15747)   on 2012-08-17 18:55:42 (Show Source): You can put this solution on YOUR website! professor announces that course grades will be computed by taking 40% of a student's project score (0-100 points) and adding 60% of the students final exam score (0-100 points). If a student gets an 86 on the project, what scores can she get on the final exam to get a course grade of at least 90? : Here is one equation for this, the relationship between the project and final exam is 4:6 : x = students grade on the final exam => 90 => 90 multiply both sides by 10 344 + 6x => 900 6x => 900 - 344 x => 556/6 x => 93 on the final exam to achieve an average of 90 for the course : : You can confirm this: .4(86) + .6(93) = 90.2 (we rounded up 92.6667)