Question

The first graders at one school went on a field trip to the zoo. The total number of children and adults who went on the field trip was 115. The number of adults was $\frac{1}{4}$the number of children. Solve the system role="math" localid="1647610059556" $c+a==115,a=\frac{1}{4}c$ to find c, the number of children and a, the number of adults.

Short answer

The number of children are 92 and the number of adult tickets are 23.

Step-by-step solution

Step 1. Given Information 

The given system of equations are

$$\begin{gathered} c+a==115--\left(1\right) \\ a=\frac{1}{4}c--\left(2\right) \end{gathered}$$

Step 2. Calculation  

Substitute equation (2) in equation (1) to find the value of c.

$$\begin{gathered} c+\frac{1}{4}c=115 \\ \frac{5c}{4}=115 \\ c=92 \end{gathered}$$

Substitute the value of c in equation (2) to find the value of a.

$$\begin{gathered} a=\frac{1}{4}\left(92\right) \\ a=23 \end{gathered}$$