Question

The box office at a Movie theatre sold 206 tickets for the evening show, and collected $2,572. How many $15 adult and how many $8 child tickets were sold? Number of adult tickets sold =Number of child tickets sold =

Answer 1

STEP - BY - STEP EXPLANATION

What to find?

• Number of adult tickets sold.

,

• Number of child tickets sold.

Given:

Total number of tickets sold = 206

Amount of total ticket sold =$2572

Cost of adult ticket = $15

Cost of chold ticket =$8

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

Step 1

Model the equation.

`x+y=206\text{ ------------\lparen1\rparen}`
`15x+8y=2572----------(2)`

Step 2

Solve the above system of linear equations by any suitable methods.

Using the substitution method;

From equation (1)

x = 206 - y ---------(3)

Step 3

Substitute equation (3) into equation (2)

`\begin{gathered} 15(206-y)+8y=2572 \\ \\ 3090-15y+8y=2572 \\ \\ -7y=-518 \\ \\ y=74 \end{gathered}`

Step 4

Substitute the alue of y into equation (3) and simplify.

`\begin{gathered} x=206-y \\ x=206-74 \\ \\ x=132 \end{gathered}`

ANSWER

• Number of adult tickets sold =132

,

• Number of child tickets sold=74