Question 978505: A family has two cars. The first car has a fuel efficiency of 15 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 825 miles, for a total gas consumption of 40 gallons. How many gallons were consumed by each of the two cars that week?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! I'm going to label the two cars A and B
Car A has fuel efficiency of 15 mpg
Car B has fuel efficiency of 30 mpg
Let,
x = number of gallons of gas car A consumes
y = number of gallons of gas car B consumes
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A total of 40 gallons were consumed by the two cars, so that means,
x+y = 40
solve for y to get y = 40 - x
Car A has fuel efficiency of 15 mpg. If it uses x gallons, then it travels 15*x = 15x miles.
Car B has fuel efficiency of 30 mpg. If it uses y gallons, then it travels 30*y = 30y miles.
Combine the two and set it equal to the total miles (825):
15x + 30y = 825
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We have this system of equations
y = 40 - x
15x + 30y = 825
Use the two equations to find x and y. First start with 15x + 30y = 825. Then replace y with 40-x. Afterwards solve for x like so
15x + 30y = 825
15x + 30(40 - x) = 825
15x + 1200 - 30x = 825
-15x + 1200 = 825
-15x = 825 - 1200
-15x = -375
x = -375/(-15)
x = 25
Now that we know x = 25, use it to find y
y = 40 - x
y = 40 - 25
y = 15
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Summary:
x = 25
y = 15
The car that has an efficiency of 15 mpg uses 25 gallons of gas.
The car that has an efficiency of 30 mpg uses 15 gallons of gas.
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