Question

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 35 miles per gallon of gas. Duringone particular week, the two cars went a combined total of 925 miles, for a total gas consumption of 35 gallons. How many gallons were consumed by each ofthe two cars that week?Note that the ALEKS graphing calculator can be used to make computations easier.

Answer 1

Given:

Fuel efficiency of the first car = 20miles/gallon of gas

Fuel efficiency of the second car = 35 miles/gallon of gas

Total miles covered on a particular week = 925 miles

Total gas consumed = 35 gallons

Solution

Let the gallons of gas consumed by the first car is x, and the gallons of gas consumed by the second car be y.

From the last information, we have:

`x\text{ + y = 35}`

The distance covered by the first car in the said week is:

`\begin{gathered} =\text{ 20 }(miles)/(gallon)\text{ }*\text{ x gallons} \\ =\text{ 20x miles} \end{gathered}`

The distance covered by the second car in the said week is:

`\begin{gathered} =\text{ 35 }(miles)/(gallon)\text{ }*\text{ y gallons} \\ =\text{ 35y miles} \end{gathered}`

From the third statement, we have:

`20x\text{ + 35y = 925 }`

To obtain x and y, we can solve the equations simultaneously

`\begin{gathered} x\text{ + y = 35} \\ 20x\text{ + 35y = 925} \end{gathered}`

Solving simultaneously, we have:

`x\text{ = 20 , y = 15}`

Answer:

First car: 20 gallons

Second car: 15 gallons