Respuesta :
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:
[tex]5.40C+9.40A=1171.20[/tex]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:
[tex]\begin{cases}C+A=148\\ 5.4C+9.4A=1171.2\end{cases} [/tex]We'll solve for the number of children C using the elimination method.
Multiply the first equation by a factor of 9.4.
[tex]\begin{cases}9.4C+9.4A=1391.2 \\ 5.4C+9.4A=1171.2\end{cases}[/tex]Subtract the second equation from the first, such that we get
[tex]\begin{gathered} 9.4C+9.4A-(5.4C+9.4A)=1391.2-1171.2 \\ \\ 4C=220 \end{gathered}[/tex]Divide both sides of the equation by a factor of 4
[tex]C=\dfrac{220}{4}=55[/tex]Hence the number of child tickets on friday at the movie theatre was 55.
