Question

At the movie theatre, child admission is $5.40 and adult admission is $9.40. On Friday, 148 tickets were sold for a total sales of $1171.20. How many child tickets were sold that day?Number of child tickets:

Answer 1

Hello there. To solve this question, we'll have to set a system of linear equations and determine how many child tickets were sold that day at the movie theatre.

Given that child admission is $5.40 and adult admission is $9.40, at the movie theatre and knowing that, on friday, 148 tickets were sold for a total of $1171.20, we have to solve for the number of children that attended the movie theatre that day.

First, say the number of children and adults, that friday at the movie theatre, were C and A, respectively.

We know that C + A is the total number of tickets sold.

Multiplying each unknown by the price they paid for the tickets will give us another equation:

`5.40C+9.40A=1171.20`

That is, C children paid $5.40 and A adults paid $9.40, for a total of $1171.20.

Hence, we have the following system of linear equations:

`\begin{cases}C+A=148\\ 5.4C+9.4A=1171.2\end{cases}`

We'll solve for the number of children C using the elimination method.

Multiply the first equation by a factor of 9.4.

`\begin{cases}9.4C+9.4A=1391.2 \\ 5.4C+9.4A=1171.2\end{cases}`

Subtract the second equation from the first, such that we get

`\begin{gathered} 9.4C+9.4A-(5.4C+9.4A)=1391.2-1171.2 \\ \\ 4C=220 \end{gathered}`

Divide both sides of the equation by a factor of 4

`C=(220)/(4)=55`

Hence the number of child tickets on friday at the movie theatre was 55.