Question

In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.

Huong is organizing paperback and hardback books for her club’s used book sale. The number of paperbacks is $12$less than three times the number of hardbacks. Huong had $162$paperbacks. How many hardback books were there?

Short answer

The number of hadback books is $58$.

Step-by-step solution

Step 1. Given Information 

We are given that Huong had $162$paperbacks.

We have to find the number of hardback books.

Step 2. Forming the equation 

Let the total number of Hardback books be x,

We know that the number of paperbacks is$12$less than three times the number of hardbacks.

So, the equation will be,

$3x-12=162$

Step 3. Solving the equation 

Adding $12$both sides, we get

$$\begin{gathered} 3x-12=162 \\ 3x=162+12 \\ 3x=174 \end{gathered}$$

Now, dividing by $3$, we get

$$\begin{gathered} x=\frac{174}{3} \\ x=58 \end{gathered}$$

Hence, the number of hadback books is $58$.

Step 4. Checking the solution 

Putting the value ofxin the equation, we get

$$\begin{gathered} 3x-12=162 \\ 3\left(58\right)-12=162 \\ 174-12=162 \\ 162=162 \\ LHS=RHS \end{gathered}$$

Hence the solution is correct.