Question

PLEASE HELP

A family has two cars. The first car has a fuel efficiency of 25 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. During one particular week, the two cars went a combined total of 1375 miles, for a total gas consumption of 65 gallons. How many gallons were consumed by each of the two cars that week?

Answer 1

Hello!

The answer is:

First car: 40 gallons consumed

Second car: 25 gallons consumed

Why?

We can solve this problem by using a 2 x 2 system of equations. Let's pose the equations that will help us to determinate what we need to know.

Calculations

Y = gallons consumed by the first car

Z = gallons consumed by the second car

We know from the statement that both cars combine a 1375 miles travel.

So, for the 1st equation we have

`25Y+15Z=1375 mi.`

We also know that both cars consume a total of 65 gallons.

So, for the 2nd equation we have

`Y+ Z = 65 gallons`

`Z=65-Y`

By substituting the 2nd equation in the 1st equation, we have

`25Y+15(65-Y)=1375`

`25Y +975-15Y=1375\\\\10Y=1375-975\\\\10Y=400\\\\Y=(400)/(10) = 40 gal.`

So, we have that the first car consumption is 40 gallons.

To know the second car consumption, we just need to substitute Y in the 2nd equation,

By substituting, we have

`40+Z=65\\\\Z=65-40=25 gal`

The second car consuption is 25 gallons.

Have a nice day!