Question

A family has 2 cars. during one week the first car consumed 30 gallons of gas and the second consumed 25 gallons of gas. the 2 cars drove a combined total of 975 miles, and the sum of their fuel efficiences are 35 miles per gallon. what were the fuel efficiency of each of the cars that week.

Answer 1

We have to write the system of equations and find the solution.

Our variables are the miles of each car in one week, so we call x for car 1 and y for car 2 the miles that each car drove.

One equation is that the two cars drove a combined total of 975 miles, so:

`x+y=975`

And the other equation, is that ths sum of their fuel efficiences are 35 miles per gallon. Also, we know that car 1 consumed 25 gallons in one week and car 2 consumed 30 gallons on one week, so:

`(x)/(25)+(y)/(30)=35`

To find the solution we can isolate x from the first equation and replace into the second equation:

`\begin{gathered} x+y=975 \\ x=975-y \end{gathered}`

Replacing into second equation and isolate y: