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

label Algebra
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A family has 2 cars. The 1st car has a fuel efficiency of 20 mpg and the 2nd car has one of 15 mpg of gas.

During one week, the two cars went a combined total of 825 miles for a total gas consumption of 45 gals

How many gallons were consumed by each of the two cars that week? 

Nov 14th, 2015

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

Lets assume fuel consumed by 2nd car = x

                        "          "           "    1st car = 45-x

Now,

Total distance traversed = 825 = 20(45-x) + 15*x

=> 825 = 900 -20x +15x

=> x = 75/5 = 15

Hence 1st car consumed = 45-15 = 30 gals of gas

And 2nd car consumed    = 15 gals if gas.

Please let me know if you need any clarification. I'm always happy to answer your questions.
Nov 14th, 2015

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