Question

Movie ticket sales are as follows: Adult: 20 tickets for $250 Child: 15 tickets for $71.25 Senior: 5 tickets for $37.50 How much does one (1) CHILD ticket cost? $7.12 per ticket $56.25 per ticket

Answer 1

The movie tickets are sold as per age groups classified into " Adult " and " Child " and " Senior ".

The movie theater compiles its sales as follows:

`\begin{gathered} \text{\textcolor{#FF7968}{Group : Number of Tickets Sold : Sales}} \\ \text{Adult : 20 : \$250} \\ \text{Child : 15 : \$71.25} \\ \text{Senior : 5 : \$37.50 } \end{gathered}`

We need to determine the cost of one child ticket. To determine the rate of a child ticket to the theater using ratios as follows:

`\begin{gathered} \text{\textcolor{#FF7968}{Number of tickets sold ( Child ) : Sales ( Child )}} \\ \text{ 15 : \$71.25} \\ \text{ 1 : x} \end{gathered}`

The above formulation shows that for 15 child tickets sold the theater earned $71.25. The next mathematical expression shows that if 1 child ticket was sold then (x) will the the amount earned.

We will cross multiply-( direct proportions ) the above formulation and solve for ( x ) as follows:

`\begin{gathered} 15\cdot x\text{ = }71.25\cdot1 \\ x\text{ = }(71.25)/(15) \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = \$4.75 per ticket}} \end{gathered}`

Therefore, the rate of one child ticket charged by the movie theater would be:

`\text{\textcolor{#FF7968}{ \$4.75 per ticket}}`