A family has two cars. The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 1650 miles, for a total gas consumption of 65 gallons. How many gallons were consumed by each of the two cars that week? Firstcar:gallons= Secondcar:gallons=

First car: 30 gallons

Second car: 35 gallons

Step-by-step explanation:

Hi, to answer this question we have to write a system of equations:

Total gas consumption was 65:

x+y=65

Where:

x = gallons consumed by the first car

y = gallons consumed by the second car

The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas, the two cars went a combined total of 1650 miles:

x 20+y 30 = 1650

The system is:

x+y=65 (1)

x 20+y 30 = 1650 (2)

Isolating y on (1)

y = 65-x

Replacing y= 65-x on (2):

x 20+(65-x)30 = 1650

20x +1,950-30x= 1650

20x-30x= 1650-1950

-10x= -300

x= -300/-10

x = 30 gallons

Back to (1)

y =65-x

y =65-30

y= 35 gallons

Feel free to ask for more if needed or if you did not understand something.  

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step-by-step explanation: there is no picture