Chapter 8, Problem 5QC

To determine

To solve: how many gallons does Martin’s tank hold.

Answer to Problem 5QC

Martin’s tank hold 27 gallons of gas.

Explanation of Solution

Given information:

Martin used $\frac{1}{3}$ of a tank of a gas in his truck to get to work. He began with full tank of gas and is left with 18 gallons of gas..

Calculation:

Let the Martin’s tank hold be $x$ gallons.

Since, he used $\frac{1}{3}$ of the tank to get to work. Therefore, gas used is $\frac{1}{3}x$ . And gas left is 18 gallons.

Now,

  $\text{Total gas}-\text{Gas used}=\text{Gas left}$

Therefore,

  $x-\frac{1}{3}x=18$ …… (1)

The least common denominator is 3. Therefore multiply the above equation with 3 and solve:

  $\begin{array}{l}x-\frac{1}{3}x=18\\ 3\cdot x-3\cdot \frac{1}{3}x=3\cdot 18\\ 3x-x=54\\ 2x=54\\ x=\frac{54}{2}\\ x=27\end{array}$

Hence,

Martin’s tank hold 27 gallons of gas.