Question

Translate to a system of equations and solve:

A science center sold 1,363 tickets on a busy weekend. The receipts totaled \(12,146. How many \)12 adult tickets and how many $7 child tickets were sold?

Short answer

The number of adult tickets and child tickets sold were 521 and 842 respectively.

Step-by-step solution

Step 1. Given Information 

The given data is that a science center sold 1,363 tickets on a busy weekend. The receipts totaled $12,146.

Step 2. Calculation 

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

The total number of tickets is 1363 that is $x+y=1363--\left(1\right)$

The cost of adult ticket is $12 and cost of child ticket is $7 and total amount received from all receips were $12146 that is $12x+7y=12146--\left(2\right)$

Multiply the equation (1) with 7 and write the revised equation.

$$\begin{gathered} 7(x+y)=7\left(1363\right) \\ 7x+7y=9541--\left(3\right) \end{gathered}$$

Solve equations (2) and (3) by subtracting equation (3) from equation (2),

$$\begin{gathered} 12x+7y-7x-7y=12146-9541 \\ 5x=2605 \\ x=521 \end{gathered}$$

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

$$\begin{gathered} 521+y=1363 \\ y=842 \end{gathered}$$