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

Algebra
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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?
Dec 18th, 2015

Thank you for the opportunity to help you with your question!

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

Please let me know if you need any clarification. I'm always happy to answer your questions.
Dec 18th, 2015

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