A family has two cars. The first car has a fuel efficiency of 15 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 1125 miles, for a total gas consumption of 55 gallons. How many gallons were consumed by each of the two cars that week?

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Polyblock Polyblock · Answer 1 · 2021-10-24T21:10:56+02:00

Answer:

First car consumed 25 gallons

Second car consumed 30 gallons

Step-by-step explanation:

Let x = first car gallons

y = second car gallons

15x + 25y = 1125

x + y = 55

Let's use substitution method

Subtract both sides of the bottom equation by y

x + y = 55

- y - y

x = 55 - y

Plug in the new x into the top equation

15(55 - y) + 25y = 1125

825 - 15y + 25y = 1125

10y + 825 = 1125

Subtract 825 from both sides

10y + 825 = 1125

- 825 - 825

10y = 300

Divide by sides by 10

10y/10 = 300/10

y = 30

The second car consumed 30 gallons

Plug in the new y into one of the original equations; let's use the bottom one

x + 30 = 55

- 30 - 30

x = 25

The first car consumed 25 gallons