Question

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

Jeff is lining up children’s and adult bicycles at the bike shop where he works. The number of children’s bicycles is nine less than three times the number of adult bicycles. There are $42$adult bicycles. How many children’s bicycles are there?

Short answer

The number of children’s bicycles is $117$.

Step-by-step solution

Step 1. Given Information 

We are given that the number of adult bicycles is $42$.

We have to find the number of children’s bicycles.

Step 2. Forming the equation 

Let the total number of children’s bicycles be xand the number of adult bicyles bey,

We know that the number of children’s bicycles is nine less than three times the number of adult bicycles.

So, the equations will be,

$$\begin{gathered} y=42 \\ x=3y-9 \end{gathered}$$

Step 3. Solving the equation 

Putting the value of yin the equation, we get

$$\begin{gathered} x=3y-9 \\ x=3\left(42\right)-9 \\ x=126-9 \\ x=117 \end{gathered}$$

Hence, the number of children’s bicycles is$117$.

Step 4. Checking the solution 

Putting the value of xin the equation, we get

$$\begin{gathered} x=3y-9 \\ 117=3\left(42\right)-9 \\ 117=126-9 \\ 117=117 \\ LHS=RHS \end{gathered}$$

Hence the solution is correct.