Answer :
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:[tex]A\ family \ has \ two \ cars. \ The \ first \ car \ has \ a \ fuel \ efficiency \ of \ 40\ miles \ per \ gallon \ of \ gas[/tex][tex]and\ the\ second\ has\ a\ fuel\ efficiency\ of\ 25\ miles\ per\ gallon\ of\ gas.[/tex] [tex]During\ one\ particular\ week,\ the\ two\ cars\ went\ a\ combined\ total\ of\ 2150\ miles,[/tex][tex]for\ a\ total\ gas\ consumption\ of\ 65\ gallons.[/tex][tex]How\ many\ gallons\ were\ consumed\ by\ each\ of\ the\ two\ cars\ that\ week?[/tex]
Now, to find the gallons consumed by each cars that week.
Let the gallons consumed by first car be [tex]x.[/tex]
And let the gallons consumed by second car be [tex]y.[/tex]
So, total gallons consumed by both cars:
[tex]x+y=65\\\\y=65-x\ \ \ \ ......(1)[/tex]
Now, the combined total miles both cars went:
[tex]x(40)+y(25)=2150[/tex]
Substituting the value of [tex]y[/tex] from equation (1):
[tex]x(40)+(65-x)(25)=2150\\\\40x+1625-25x=2150\\\\1625+15x=2150[/tex]
Subtracting both sides by 1625 we get:
[tex]15x=525[/tex]
Dividing both sides by 15 we get:
[tex]x=35.[/tex]
The gallons consumed by first car = 35.
Now, to get the gallons consumed by second car by substituting the value of [tex]x[/tex] in equation (1):
[tex]y=65-x\\\\y=65-35\\\\y=30.[/tex]
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.