# Need algebra help for solving a value mixture problem using a system of linear equations

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### Question Description

A family has 2 cars.  The 1st has a fuel efficiency of 15 mpg the 2nd 35 mpg.  During one week, the cars went a combined total of 1450 miles, for a total gas  consumption of 50 gals. How many gallons were used consumed by each car that week?

School: UC Berkeley

family has 2 cars

1st fuel efficiency=15 mpg

2nd fuel efficiency=35 mpg

total distance=1450 miles

total consumption=50 gal

lets get the gallons consumed by 1st car as x

then the gallons consumed by 2nd car=50-x

so we can write

total distance=15*x+(50-x)35

1450=15x+35*50-35x

20x=1750-1450

20x=300

x=15 g

so 50-x=35 g

the gas  consumed by 1st car=15 gallons

the gas  consumed by 2nd car=35 gallons

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Anonymous
Goes above and beyond expectations !

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