Question

Translate to a system of equations and solve:

The ticket office at the zoo sold 553 tickets one day. The receipts totaled \(3,936. How many \)9 adult tickets and how many $6 child tickets were sold?

Short answer

The number of adult tickets and child tickets sold were 206 and 347 respectively.

Step-by-step solution

Step 1. Given Information

The given data is that the ticket office at the zoo sold 553 tickets one day. The receipts totaled $3,936.

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 553 that is $x+y=553--\left(1\right)$

The cost of adult ticket is $9 and cost of child ticket is $6 and total amount received from all receips were $3936 that is $9x+6y=3936--\left(2\right)$

Multiply the equation (1) with 6 and write the revised equation.

$$\begin{gathered} 6(x+y)=6\left(553\right) \\ 6x+6y=3318--\left(3\right) \end{gathered}$$

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

$$\begin{gathered} 9x+6y-6x-6y=3936-3318 \\ 3x=618 \\ x=206 \end{gathered}$$

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

$$\begin{gathered} 206+y=553 \\ y=553-206 \\ y=347 \end{gathered}$$