# Questions on Word Problems: Linear Equations And Systems Word Problems answered by real tutors!

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 Linear Solvers Practice Answers archive Word Problems Lessons In depth

Question 752451: Reversing the digits of Gyver's age gives Ed's age with a difference of 18 years. If the sum of the digits of each age is 6, how old is Gyver?
Thanks a bunch for answering this :)

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Reversing the digits of Gyver's age gives Ed's age with a difference of 18 years. If the sum of the digits of each age is 6, how old is Gyver?
Thanks a bunch for answering this :

Based on info, Gyver is YOUNGER than Ed

Let the tens and units digits of Gyver’s age be T and U, respectively
Then: 10T + U = 10U + T – 18 ------ 10T – T + U – 10U = - 18 ----- 9T – 9U = - 18 ---- 9(T – U) = 9(- 2)
T – U = - 2 ------ eq (i)
Also, T + U = 6 ----- eq (ii)
2T = 4 ------ Adding eqs (i) & (ii)
T, or tens digit of Gyver’s age = , or 2

2 – U = - 2 ------ Substituting 2 for T in eq (i)
- U = - 2 – 2
- U = - 4
U, or units digit of Gyver’s age = , or 4

Therefore, Gyver is years-old

You can do the check!!

Question 752327: Find the selling price per kg of a coffee mixture made from 8 kg of coffee that sells for $24 per kg and 12 kg of coffee that costs$20 per kg

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The selling price of the mixture is $21.60 / kg Question 752328: Ten grams of sugar are added to a 40 grams serving of a breakfast cereal that is 30% sugar. What is the percent concentration of sugar in the resulting mixture? Answer by josmiceli(9697) (Show Source): You can put this solution on YOUR website! grams of sugar in the cereal Let = the fraction of sugar in resulting mixture ------------- 44 percent of the final mixture is sugar Question 752274: 2 and a half hours plus three and three-quarter hours plus two thirds of an hour at$45 an hour, what Is the total amount earned?
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$311.25 was earned If you're not allowed to use decimals, you have to do something like this: OK Question 752246: In 1994, the moose population in a park was measured to be 3550. By 1998, the population was measured again to be 3270. If the population continues to change linearly: Find a formula for the moose population, P, in terms of t, the years since 1990.What does your model predict the moose population to be in 2007? Having trouble solving this problem. Answer by josmiceli(9697) (Show Source): You can put this solution on YOUR website! Call the year 1990 Then, 1994 = and, 1998 = ------------------- Now you have 2 points on a straight line: ( 4, 3550 ) ( 8, 3270 ) Plug these points into the general point-slope formula ------------------- In 2007, ------------- check: ( 8,3270 ) OK You can check the other point Question 752091: I have been trying to turn this word problem into a linear equation for a week now with no success. Can you help? A downtown employee is looking for the best option for parking a car during a 5 day work week. Garage A offers unlimited parking at a flat rate$150.00 per month. Garage B offers an hourly rate of $5.00 for parking. Which option is best for the employee on a monthly basis? The employee is parking 160 hours per month. This is a word problem that I had to come up with on my own make 2 linear equations out of it and then graph it and show where they intercept. Any help would be appreciated. Thank you! Answer by MathTherapy(1430) (Show Source): You can put this solution on YOUR website! I have been trying to turn this word problem into a linear equation for a week now with no success. Can you help? A downtown employee is looking for the best option for parking a car during a 5 day work week. Garage A offers unlimited parking at a flat rate$150.00 per month. Garage B offers an hourly rate of $5.00 for parking. Which option is best for the employee on a monthly basis? The employee is parking 160 hours per month. This is a word problem that I had to come up with on my own make 2 linear equations out of it and then graph it and show where they intercept. Any help would be appreciated. Thank you! Garage A's charge is$150

Garage B's charge = 5H, with H being amount of hours of parking

5H < 150

H, or hours that'll make garage B's cost less than garage A's should be < , or <

This means that if a person needs to park for less than 30 hours per month, then garage B will be cheaper.

At 30 hours per month both costs are equal.

Parking for 160 hours DEFINITELY makes garage A the cheaper of the two. You can do the math to see why this is so.

You can graph garage A's linear equation as A(x) = 0x + 150, with x being the amount of monthly-hours of parking

Garage B's equation: B(x) = 5x, with x being the amount of hours of monthly-hours of parking.

You'll then see where the two equations intersect, which is the point where the two costs are equal.

Question 752066: there are 1176 students in a school. There are 50 more girls than boys. how many boys are there?
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b+g=1176
g=b+50
then b+(b+50)=1176
and so
2b=1126
b=563

:)

Question 751915: It possible solve each system of equations use any method. If there is not aa unique solutions to a system, state a reason
2x-8y=5
-6x+24y=15

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The given equations of the system(?):

The second equation,

And perform multiplication of both sides by -1,
.

Now, your system of equations really is this:
-----------------

and

----------------

What does that tell you?

Question 751842: if the mearures pf wall is 8m*5m*2m and a brick measure is 50cm *30cm*20cm.find the numbr of bricks in this wall?
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Convert wall dimensions to centimeters.
800 x 500 x 200
Multiply together
= 80,000,000 cm^3
Multiply brick dimensions
50 x 30 x 20
= 30,000
Divide 80,000,000/30,000
= 266.6 bricks
Hope this helps
:-)

Question 751838: The fair of hiring a taxi is Rs.7/km and a car is Rs.6/km..if the total cost of travelling is Rs.595..what is the no of kms traveled by taxi..?
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If hiring a taxi costs Rs. 7/km and
the total cost is Rs 595 then the
number of kms.travelled will be:
595/7 = 85 kms

Question 751272: Sam takes 2 hours longer to complete his taxes then Emily.
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Question 751004: A local computer center charges nonmembers $5 per session to use the media center. If you pay a membership fee of$25, you pay
only $3 per session. Write an equation that can help you decide whether to become a member. Then solve the equation and interpret the solution Answer by Edwin McCravy(8913) (Show Source): You can put this solution on YOUR website! A local computer center charges nonmembers$5 per
session to use the media center. If you pay a membership fee of $25, you pay only$3 per session. Write an equation that can help you decide whether to
become a member. Then solve the equation and interpret the solution.
Let N = the number of sessions you will need.

If you don't become a member then your total cost for
the N sessions will be $5N If you do become a member then your total cost for the N sessions will be$25 + $3N Now we set those equal to each other to find the value of N when they will cost the same. 5N = 25 + 3N That's the equation. We solve it 2N = 25 N = 12.5 That's halfway between two integers, 12 and 13. Interpretation. If you will need 12 or fewer sessions, then you should not become a member. But if you will need 13 or more sessions, then you should become a member. Edwin Question 750578: 45% of the 600 seats were filed. How many people were already in the theater Found 2 solutions by dkppathak, stanbon: Answer by dkppathak(43) (Show Source): You can put this solution on YOUR website! 45%seats filled filled seat are 270 already people available in side hall are 100-45 =55% 55/100 of 600=330 330 were already in side answer 330 Answer by stanbon(57409) (Show Source): You can put this solution on YOUR website! 45% of the 600 seats were filled. How many people were already in the theater ----- Ans: # filled = 0.45*600 = (45/100)600 = 45*6 = 240+30 = 270 ================ Cheers, Stan H. ================ Question 750438: A garage bill was £346.50. The labour cost £187.60 more than the parts. How much does the labour cost? Answer by checkley79(3054) (Show Source): You can put this solution on YOUR website! P+L=346.50 L=P+187.60 P+(P+187.60)=346.50 2P=346.50-187.60 2P=158.90 P=158.90/2 P=$79.45 WAS THE COST OF THE PARTS.
L=79.45+187.60
L=$267.05 WAS THE COST OF THE LABOR. PROOF: 267.05+79.45=346.50 346.50=346.50 Question 750334: 20 man can finish a work in 30 days.after how many days should 5 people goes the work will be fished in 35 days? Answer by josgarithmetic(1540) (Show Source): You can put this solution on YOUR website! First find the rate of 1 man. The rates of each man working at the same time as another are simply additive. 20 men do 1 job in 30 days. 1 man does 1/20 job in 30 days. Think about how that should make sense. WHAT IS THIS ONE-MAN RATE? His rate of work is jobs per day. This is jobs per day. Now, your question was, not comprehendible. What are you asking for? Five men working, and how many days needed for them to do the job? Why did you mention 35 days? Trying to calculate the number of days for the 5 men: , where r is rate of work, t is days, j is amount of jobs, But be sure to see that rate for 5 men is jobs per day. =120 days. That may have been not what you wanted to ask. Question 750382: What is the decrease percentage from 15 to 10? Answer by Alan3354(30993) (Show Source): You can put this solution on YOUR website! What is the decrease percentage from 15 to 10? ------------ 100*(15 - 10)/15 = 100/3 % =~ 33% Question 750136: Internet Company A charges a$25 fee plus an additional $0.35 per hour. Internet Company B charges a$10 fee plus an additional $0.50 per hour. For what number of hours are the charges for both companies the same? Found 3 solutions by tommyt3rd, JoeTaxpayer, dkppathak: Answer by tommyt3rd(614) (Show Source): You can put this solution on YOUR website! First we write their total charges as equations. Then we solve for t - the number of hours when both charges are equal When they charge the same A=B and we can write so t=100 hours :) Answer by JoeTaxpayer(145) (Show Source): You can put this solution on YOUR website! 2500+35X=1000+50X 1500=15X (I simplified by subtracting 1000 and 35X from both sides) X=100 ANS 100 Hours Note: setting the problem up as 'cents' helped avoid using decimals or fractions. Answer by dkppathak(43) (Show Source): You can put this solution on YOUR website! let extra hours are y hrs for a company 25+.35y for B company 10+.50y as per conditions both value are equal therefor 25+.35y=10+.50y 15=.15y y=15/.15=100 100hours answer 100 hours Question 750029: If person A and B has a total of 192. If person A given person B$30, person B will have twice as much as person A, how much person A and person B has?
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let A has x then B has 192-x
A give person B $30, person B will have twice as much as person A so 192-x+30=2(x-30) or 222-x=2x-60 or 3x=282 or x=94 A has B has 192-94=98 Question 750087: if a certain number of 2 digits is divided by the sum of its digits the quotient is 3 and remainder is 7 . If the digits are interchanged and the resulting number is divided by the sum of digits the quotient is 7 and the remainder is 3. Find the number. Answer by dkppathak(43) (Show Source): You can put this solution on YOUR website! let unit place is y and tens place is x of two digit number number 10x+y and reverse number will be 10y+x as per given conditions 10x+y=3(x+y)+7 and 10y+x +7(x+y)+3 solving these equations we can get as 7x-2y=7 i -6x+3y=3 ii by solving both equations elimination method we will get X=3 and Y=7 two digit number whose tens place is 3 and unit place is 7 two digit number is 37 answer 37 Question 749762: a small tree was planted at a height of 7 feet. the tree has been planted for 14 month, and is now 54.6 feet tall. which equation could be used to find X, the average number of feet the tree grow in each month? Answer by stanbon(57409) (Show Source): You can put this solution on YOUR website! a small tree was planted at a height of 7 feet. the tree has been planted for 14 month, and is now 54.6 feet tall. which equation could be used to find X, the average number of feet the tree grow in each month? ------- f(0) = 7 is the starting point f(14) = 54.6 ----- average growth per month = slope = 54.6/14 = 3.9 ------ Equation: f(x) = 3.9x + 7 ---- Cheers, Stan H. ============= Question 749638: You buy a total of 50 turkey burgers and veggies burgers for$90. You pay $2 per turkey burger and$1.50 per veggie burger.
I have to write 2 equations to represent the situation then solve them. I have come up with 2t + v= $90 and t + 1.50= 50 which I then subtracted the two equations and came out with v=5 and t=42.5 which can't be the answer since their is a total of 50. Thank you for you time :) Answer by MathTherapy(1430) (Show Source): You can put this solution on YOUR website! You buy a total of 50 turkey burgers and veggies burgers for$90. You pay $2 per turkey burger and$1.50 per veggie burger.
I have to write 2 equations to represent the situation then solve them. I have come up with 2t + v= $90 and t + 1.50= 50 which I then subtracted the two equations and came out with v=5 and t=42.5 which can't be the answer since their is a total of 50. Thank you for you time :) Let the amount of turkey and veggie burgers bought be T, and V, respectively. Then: You should be able to solve the system of equations to determine the amount of turkey &/or veggie burgers that were purchased. Question 749612: A kicker on a football team scores 1 point for making an extra point and 3 points for making a field goal. The kicker makes a total of 8 extra points and field goals in one game. He scored a total of 12 points in the game. I have to write 2 equations representing the situation and solve them. I think I will be able to solve them but I can't come up with the equations. 1x + y =8 3x + y =12, is all I am able to come up with. Your time is greatly appreciated. (: Answer by ankor@dixie-net.com(15661) (Show Source): You can put this solution on YOUR website! A kicker on a football team scores 1 point for making an extra point and 3 points for making a field goal. The kicker makes a total of 8 extra points and field goals in one game. He scored a total of 12 points in the game. I have to write 2 equations representing the situation and solve them. I think I will be able to solve them but I can't come up with the equations. 1x + y =8 3x + y =12 : rewrite it to 3x + y = 12 x + y = 8 -------------Subtraction eliminates y, find x 2x = 4 x = 4/2 x = 2 field goals I'm sure you can find the extra points Question 749615: You have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. Write two equations to represent the situation. Answer by tommyt3rd(614) (Show Source): You can put this solution on YOUR website! m-# of math s-# of science m+s=42 m=s+10 :) Question 749577: Michelle is making goodie bags for Christmas filled with chocolates and candy. Chocolates cost$3.00 per lb. Candy cost $2.00 per lb. Michelle bought a total of 15 pounds of candy and chocolate and spent$40. How many pounds did she buy of each?
Found 2 solutions by Edwin McCravy, richwmiller:
Answer by Edwin McCravy(8913)   (Show Source):
You can put this solution on YOUR website!
Michelle is making goodie bags for Christmas filled with chocolates and candy. Chocolates cost $3.00 per lb. Candy cost$2.00 per lb. Michelle bought a total of 15 pounds of candy and chocolate and spent $40. How many pounds did she buy of each? She bought x pounds of chocolates at$3 a pound, so those x pounds of chocolates cost her $3x dollars. She bought 15-x pounds of chocolates at$2 a pound, so those 15-x pounds of chocolates cost her $2(15-x) dollars. 3x + 2(15 - x) = 40 3x + 30 - 2x = 40 x + 30 = 40 x = 10 Edwin Answer by richwmiller(9143) (Show Source): You can put this solution on YOUR website! x+y=15 3x+z*y=40 We have three unknowns and only two equations. An integer solution is x = 10, y = 5, z = 2 Question 749568: the fraction of t on top and -2 at the bottom and -1 =4 i need searious HELP PLEASE!! Answer by unlockmath(1603) (Show Source): You can put this solution on YOUR website! Hello, Let's write this as: t/(-2)+(-1)=4 Multiply by -2 to get: t+2=-8 Subtract 2: t=-10 Make sense? RJ www.math-unlock.com Question 749250: The algebraic expression 0.75(220-A) gives the target heart rate for beneficial excercise for men, where A is the age of the man. Find the target heart rate for a 73-year old man. Round your answer to the nearest whole number Please help solve Answer by solver91311(16897) (Show Source): You can put this solution on YOUR website! Write in pencil. Erase the A. Write 73 in place of the A you just erased. Do the indicated arithmetic. John Egw to Beta kai to Sigma My calculator said it, I believe it, that settles it Question 749236: dina planted an eight foot tree in her backyard which she expects to grow at a rate of 4 feet per year. Determine th eequation of the line that shows how tall the tree will be each year. Please help solve this problem ! Answer by josmiceli(9697) (Show Source): You can put this solution on YOUR website! Plot the height in feet on the vertical axis and time in years on the horizontal axis. The general form of the equation will be = slope = h-intercept -------------------------- Call the time when she plants the tree. You now have the point ( 0,8 ) This is the h-intercept The slope of the line is the rate of growth of the tree So, the equation is Question 749015: The scale on a map indicates that 4cm is equivalent to 10 miles. If the distance between two cities on the map is 11cm, how far apart are the two cities? Answer by Cromlix(353) (Show Source): You can put this solution on YOUR website! If 4cm is equivalent to 10 miles 1 cm is equivalent to 10/4 or 5/2 miles 11 cm is equivalent to 11 x 5/2 = 55/2 or 27.5 miles Question 749020: a foot-long hot dog is cut into two parts. One part is 2 inches longer than the other part, How long are the two parts Answer by Cromlix(353) (Show Source): You can put this solution on YOUR website! The two lengths x and x + 2 Therefore x + (x + 2) = 12 inches 2x + 2 = 12 inches 2x = 12 - 2 2x = 10 x = 5 Therefore the two lengths are 5 inches and (5 + 2 inches)7 inches. Bon appetit! Question 749021: please help me to solve this question.the prize of 15 books is rs 6750.how many books can be purchased for rs 4050? Answer by Cromlix(353) (Show Source): You can put this solution on YOUR website! 15 books cost rs 6750 1 book costs rs 450 (6750/15) 9 books cost rs 4050 (4050/450 = 9) Hope this helps. Question 748986: twelve cans of peaches are placed into each box.write a function rule for the number of boxes needed for c cans.how many boxes are needed for 1440 cans? Answer by timvanswearingen(106) (Show Source): Question 748648: Hello, What would be the answer to the question below and how would I put the word problem including the answers into a linear equation? Would there be any way at all that you could please break it down step by step so that I can understand it better? Thank you A mom bought 28 packages of Reese’s Cups with 88 total cups. Each king size package holds 4 cups. Each regular size package holds two cups. How many of each size did she buy? Found 2 solutions by MathTherapy, rothauserc: Answer by MathTherapy(1430) (Show Source): You can put this solution on YOUR website! Hello, What would be the answer to the question below and how would I put the word problem including the answers into a linear equation? Would there be any way at all that you could please break it down step by step so that I can understand it better? Thank you A mom bought 28 packages of Reese’s Cups with 88 total cups. Each king size package holds 4 cups. Each regular size package holds two cups. How many of each size did she buy? Let amount of king-sized, and regular-sized Reese’s she bought be K, and R, respectively Then: K + R = 28 ------ eq (i) Also, 4K + 2R = 88 ----- eq (ii) - 2K – 2R = - 56 ------ Multiplying eq (i) by – 2 ----- eq (iii) 2K = 32 ----- Adding eqs (ii) & (iii) K, or amount of king-sized Reese’s purchased = , or 16 + R = 28 ------- Substituting 16 for K in eq (i) R, or amount of regular-sized Reese’s purchased = 28 – 16, or You can do the check!! Send comments and “thank-yous” to “D” at MathMadEzy@aol.com Answer by rothauserc(210) (Show Source): You can put this solution on YOUR website! we are given the following problem: A mom bought 28 packages of Reese’s Cups with 88 total cups. Each king size package holds 4 cups. Each regular size package holds two cups. How many of each size did she buy? let x be the number of king size packages and y be the number of regular size packages, then we have x+y=28 4x+2y=88 solve the first equation for x, x=28-y then substitute for x in the second equation 4*(28-y)+2y=88 112-4y+2y=88 -2y=-24 y=12 and x = 16 she bought 16 king size packages and 12 regular size packages Question 748686: on the grand opening of the movie theater 172 tickets were sold adult tickets is$16 and a child ticket is $8 . "how do you put this in a problem"? Answer by Cromlix(353) (Show Source): You can put this solution on YOUR website! In this problem you also require a sum of money which equals the cost of all the tickets sold. First line would be: x + y = 172 x representing an adult's ticket y representing a child's ticket Then: 16x + 8y = cost of all tickets sold x + y = 172 16x + 8y = cost of all tickets sold Solve this by substitution Question 747923: A Grocery store sells 4000 bags ( 4 litres each) of milk per week when the price is$5.50 for a bag. Customer research indicates that for each $0.10 decrease in the price, 200 more bags of milk will be sold. The store wants to bring in$27,500 for the bags. What price should the grocery store charge?

a) Set up the solution with let statements and an algebraic expression.

b) Use the quadratic formula to determine the roots of the equation.

c) How many price decreases would be required for the store to bring in $30,000? d) What would the price need to be for the bag of milk and how many bags would be sold at the store? Please help me. My dad ( who works as a Soils Engineer) and I have tried for four hours and haven't gotten an answer that actually works. Please help me Answer by JoeTaxpayer(145) (Show Source): You can put this solution on YOUR website! Let N equal the number of 10 cent price drops. Bags that will be sold = 4000+200N New price per bag = 5.50-.1N Revenue = (4000+200N)(5.5-.1N) R = 22000+1100N-400N-20N^2 R = -20N^2+700N+22000 This is a downward facing parabola. We aren't interested in the zeros, but in the maximum as we wish to maximize dollars. The vertex is at -b/2a = -700/(2*-20) = 17.5 The equation doesn't care that it started with a dime change to move sales. The maximum revenue is at 5.50 - 1.75 =$3.75 and 4000+200(17.5) = 7500 bags sold, for max revenue 7500*3.75 = $28125 I solved max revenue, you can't get over$30,000. Set R=$27,500 and solve if you'd like. Question 747698: 5 man do a work in 30 days .how many man needed to do that work in 1 day Answer by Cromlix(353) (Show Source): You can put this solution on YOUR website! 5 men can do a job in 30 days 150 men can do the job in 1 day. Question 747250: Suppose that a line models the amount of water in a swimming pool. What does a positive slope indicate? What does a negative slope indicate" Answer by ankor@dixie-net.com(15661) (Show Source): You can put this solution on YOUR website! Positive slope, filling the pool Negative slope, draining the pool Question 747249: If they bought one peppermint pattie, One lollipop, and One gumdrop, the total 21 cents and you found that it costs the same amount of money to buy 2 peppermint patties & 1 gumdrop costs 2 cents more than a lollipop find out the cost of each kind of candy Answer by ankor@dixie-net.com(15661) (Show Source): You can put this solution on YOUR website! If they bought one peppermint pattie, One lollipop, and One gumdrop, the total 21 cents; and you found that it costs the same amount of money to buy 2 peppermint patties; & 1 gumdrop costs 2 cents more than a lollipop find out the cost of each kind of candy : "they bought one peppermint pattie, One lollipop, and One gumdrop, the total 21 cents" p + l + g = 21 : "it costs the same amount of money to buy 2 peppermint patties" 2p = 21 p = 21/2 p = 10.5 for one peppermint then 10.5 + l + g = 21 l + g = 21 - 10.5 l + g = 10.5 : "1 gumdrop costs 2 cents more than a lollipop" g = l + 2 -l + g = 2 : Add the last two equations l + g = 2 -l+ g = 10.5 ------------Adding eliminates l, find g 2g = 12.5 g = 12.5/2 g = 6.25 for one gum drop : l + 6.25 = 10.5 l = 10.5 - 6.25 l = 4.25 for one lollipop : : See if this checks out 10.5 + 6.25 + 4.25 = 21 Question 747221: How many ounces would be required to cover a 4, 000 square-foot lawn? Answer by Alan3354(30993) (Show Source): You can put this solution on YOUR website! How many ounces would be required to cover a 4, 000 square-foot lawn? ----------------- Not enough info. Question 747082: Solve the system of equations: 3x - y = 9 and 6x + y = 0 Answer by lenny460(778) (Show Source): You can put this solution on YOUR website! Solve the system of equations: 3x - y = 9 and 6x + y = 0 We can solve the above using the Addition Method: 3x - y = 9 6x + y = 0 Add the above two equations together: 3x - y + 6x + y = 9 + 0 Combine like terms: 3x + 6x = 9x -y + y = 0 9 + 0 = 9 We now have: 9x = 9 x = 1 Substitute x = 1 into the first equation 3x - y = 9 3(1) - y = 9 3 - y = 9 Subtract 3 from each side of the equation. 3 - y - 3 = 9 - 3 Combine like terms: 3 - 3 = 0 9 - 3 = 6 -y = 6 Divide each side by -1 -1y/-1 = 6/-1 y = -6 Plug the x and y values into equation 2 to check: 6x + y = 0 6(1) + (-6) = 0 6 + (-6) = 0 Answer: x = 1 and y = -6 Lennox Obuong Algebra Tutor Nairobi, Kenya Email: obuong3@aol.com Question 747061: A car salesman earns$18,000 a year, plus 8% of the amount of sales from the cars he sells. What is the minimum amount of sales he must make if he wants to earn at least $40,000 per year? ***I really just need help with how to set up the problem, i can do the work, i just don't know where to start. Please help!) Answer by stanbon(57409) (Show Source): You can put this solution on YOUR website! A car salesman earns$18,000 a year, plus 8% of the amount of sales from the cars he sells. What is the minimum amount of sales he must make if he wants to earn at least $40,000 per year? ----------- Let the minimum amt. be "x": Inequality: 18000 + 0.08x >= 40000 0.08x >= 22000 x >=$275,000
===================
Cheers,
Stan H.

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830