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?

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mixter17 mixter17 · Answer 1 · 2019-01-18T01:58:46+01:00

The answer is:

First car: 40 gallons consumed

Second car: 25 gallons consumed

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.

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

[tex]25Y+15Z=1375 mi.[/tex]

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

So, for the 2nd equation we have

[tex]Y+ Z = 65 gallons[/tex]

[tex]Z=65-Y[/tex]

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

[tex]25Y+15(65-Y)=1375[/tex]

[tex]25Y +975-15Y=1375\\\\10Y=1375-975\\\\10Y=400\\\\Y=\frac{400}{10} = 40 gal.[/tex]

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

[tex]40+Z=65\\\\Z=65-40=25 gal[/tex]

The second car consuption is 25 gallons.

Have a nice day!