Question

In the following exercises, translate to a system of equations and solve.

Tickets for a show are \(70 for adults and \)50 for children. One evening performance had a total of 300 tickets sold and the receipts totaled $17,200. How many adult and how many child tickets were sold?

Short answer

The number of children tickets are 190 and number of adult tickets are 110.

Step-by-step solution

Step 1. Given Information  

The given data is that Tickets for a show are $70 for adults and $50 for children. One evening performance had a total of 300 tickets sold and the receipts totaled $17,200.

Step 2. Calculation 

Let x be the number of adult tickets and ybe the number of child tickets.

Total number of tickets is 300 that is $x+y=300--\left(1\right)$

The total amount received from all receipts is $17200 that can be expressed as $70x+50y=17200--\left(2\right)$

Multiply equation (1) with 50 and write the revised equation.

$$\begin{gathered} 50(x+y)=50\left(300\right) \\ 50x+50y=15000--\left(3\right) \end{gathered}$$

Solve the equations (2) and (3) by subtracting equation (3) from equation (2) to find the value of x.

$$\begin{gathered} 70x+50y-50x-50y=17200-15000 \\ 20x=2200 \\ x=110 \end{gathered}$$

Substitute the value of x in equation (1) to find the value of y.

$$\begin{gathered} 110+y=300 \\ y=190 \end{gathered}$$