Question 1182928: Imagine that the price per gallon of gas with a $7 car wash is $3.19 and the price without the car wash is $3.39. When is it worth it to buy the car wash? When is it worth it if the car wash costs $2?
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! price per gallon of gas with 7 dollar car wash is 3.19.
price per gallon of gas without the car wash is 3.39.
y = total price
x = number of gallons of gas.
price of car wash is 7.00.
total cost with car wash is y = 7 + 3.19 * x
total cost without car wash is y = 3.39 * x
it is worth it to buy the car wash when the total price with the car wash is less than the total price without the car wash.
the inequality for that is:
7 + 3.19 * x < 3.39 * x
subtract 3.19 * x from both sides of that equation to get:
7 <= 3.39 * x - 3.19 * x
simplify to get:
7 < .20 * x
divide both sides by .2 to get:
7/.20 < x
simplify to get:
35 < x
this is the same as:
x > 35
if the number of gallons of gas is greater than 35, then it is cheaper to buy the gas with the car wash than without.
if you buy exactly 35 gallons of gas, you will pay the same for with the car wash and without the car wash.
7.00 + 3.19 * 35 = 118.65
3.39 * x = 118.65.
if you buy 30 gallons of gas, you will pay less for without the car wash than with the car wash.
7.00 + 3.19 * 30 = 102.7
3.39 * 30 = 101.7
if you buy 40 gallons of gas, you will pay less for with the car wash than without the car wash.
7.00 + 3.19 * 40 = 134.6
3.39 * 40 = 135.6
if the car wash costs 2 dollars instead of 7, then the equations are:
y = 2 + 3.19 * x for with the car wash.
y = 3.39 * x for without the car wash.
the total cost for with the car wash will be less than the total cost without the car wash when 2.00 + 3.19 * x <= 3.39 * x
subtract 3.19 * x from both sides to get:
2 < .20 * x
divide both sides by .2 to get:
2/.2 < x
simplify to get:
10 < x
this is the same as x > 10
the break even point is when x = 10
you pay less without the car wash when x < 10
you pay less with the car wash when x > 10
when x = 10, you pay the same with or without the car wash.
2 + 3.19 * 10 = 33.9
3.39 * 10 = 33.9
when x = 9, you pay less without the car wash.
2 + 3.19 * 9 = 30.71
3.39 * 9 = 30.51
when x = 11, you pay less with the car wash.
2 + 3.19 * 11 = 37.09
3.39 * 11 = 37.29
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
The difference in the price per gallon is 20 cents.
If the car wash costs $7, then the number of gallons of gas you need to buy to save $7 on the gas is $7/$0.20 = 35.
So it is worth getting the car wash if you are buying 35 gallons or more of gas.
If the car wash costs $2, then the number of gallons of gas you need to buy to save $2 on the gas is $2/$0.20 = 10.
So it is worth getting the car wash if you are buying 10 gallons or more of gas.
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