Question

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

Answer 1

The gallons of gas consumed by the first car is 35 and the second car is 30.

Explanation:

There are some data missing in the question, so below is the question with complete data:
`A\ family \ has \ two \ cars. \ The \ first \ car \ has \ a \ fuel \ efficiency \ of \ 40\ miles \ per \ gallon \ of \ gas`
`and\ the\ second\ has\ a\ fuel\ efficiency\ of\ 25\ miles\ per\ gallon\ of\ gas.`
`During\ one\ particular\ week,\ the\ two\ cars\ went\ a\ combined\ total\ of\ 2150\ miles,`
`for\ a\ total\ gas\ consumption\ of\ 65\ gallons.`
`How\ many\ gallons\ were\ consumed\ by\ each\ of\ the\ two\ cars\ that\ week?`

Now, to find the gallons consumed by each cars that week.

Let the gallons consumed by first car be
`x.`

And let the gallons consumed by second car be
`y.`

So, total gallons consumed by both cars:

`x+y=65\\\\y=65-x\ \ \ \ ......(1)`

Now, the combined total miles both cars went:

`x(40)+y(25)=2150`

Substituting the value of
`y` from equation (1):

`x(40)+(65-x)(25)=2150\\\\40x+1625-25x=2150\\\\1625+15x=2150`

Subtracting both sides by 1625 we get:

`15x=525`

Dividing both sides by 15 we get:

`x=35.`

The gallons consumed by first car = 35.

Now, to get the gallons consumed by second car by substituting the value of
`x` in equation (1):

`y=65-x\\\\y=65-35\\\\y=30.`

The gallons consumed by second car = 30.

Hence, the gallons of gas consumed by the first car is 35 and the second car is 30.