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

Answer:

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

Step-by-step 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.