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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 35 miles per gallon of gas. During one particular week, the two cars went a combined total of 1350 miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?

Respuesta :

The fuel consumption of each of the cars during the week are as follows;

  • The first car consumes 20 gallons of fuel.
  • The second car consumes 30 gallons of fuel.

Reasons:

Fuel efficiency of the first car = 15 miles per  gallon

Fuel efficiency of the second car = 35 miles per gallon

Combined distance traveled by the two cars in a week = 1,350 miles

The total gas consumption during the week = 50 gallons

Let x represent the number of gallons consumed by the first car, and let y

represent the number of gallons consumed by the second car, we get the

following system of simultaneous equations;

  • 15·x + 35·y = 1,350...(1)
  • x + y = 50...(2)

Therefore;

y = 50 - x

Which gives;

15·x + 35 × (50 - x) = 1,350

15·x + 1,750 - 35·x = 1,350

1,750 - 1,350 = 35·x - 15·x = 20·x

400 = 20·x

x = 400 ÷ 20 = 20

  • The number of gallons consumed by the first car, x = 20 gallons

From equation (2), we have;

x + y = 50

y = 50 - x

Therefore;

y = 50 - 20 = 30

  • The number of gallons consumed by the second car, y = 30 gallons

Learn more about word problems that lead to simultaneous equations here:

https://brainly.com/question/1717365

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