Question

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

One-fourth of the candies in a bag of M&M’s are red. If there are $23$red candies, how many candies are in the bag?

Short answer

The total candies in the bag is $92$.

Step-by-step solution

Step 1. Given Information 

We are given that there are $23$red candies,

We have to find the total number of candies.

Step 2. Forming the equation 

Let the total number of choir members bex,

We know that,

$\frac{1}{4}$of total candies $=23$

So, the equation will be,

$\frac{1}{4}x=23$

Step 3. Solving the equation 

Solving the equation,

$\frac{1}{4}x=23$

Multiplying by $4$, we get

$$\begin{gathered} 4·\frac{1}{4}x=23·4 \\ x=92 \end{gathered}$$

The total candies is $92$.

Step 4. Checking the solution 

Putting the value of xin the equation, we get

$$\begin{gathered} \frac{1}{4}x=23 \\ \frac{1}{4}\left(92\right)=23 \\ 23=23 \\ \text{LHS}=\text{RHS} \end{gathered}$$

Hence the solution is correct.