Mega Movies hosted a film premiere on Friday night. They charged $8 for adults and $6 for children. One hundred seventy-four adults and children attended, and $1,342 was made in ticket sales. How many children and how many adults went to the film premiere?

Guest Mar 10, 2020

#1**0 **

174 tix total

a = adult tix revenue from adult tix = $ 8a

174-a = c = children tix revenue from child tix = $ 6 (174-a) the revenues summed = $ 1342

8a + 6 (174-a) = 1342 solve for 'a' the number of adult tix ..... then 174-a = child tix

ElectricPavlov Mar 10, 2020

#2**0 **

Let's start by assuming that everyone who went to the premiere was an adult (\(174 \) adults and \(0\) children).Then how much money would Mega Movies have made?

\(174 \cdot $8 = $1392\).

That is too much, so there must have been some children. For every adult replaced by a child, Mega Movies lost \($2\) from their total, since a child ticket cost \($2\) less than an adult ticket.

They lost a total of \($1392 - $1342 = $50\).

\({$50 \over $2} = 25\), so \(25\) children went to the film premiere.

\(174 - 25 = 149\), so the answer is:

\(149 \) adults and \(25\) children.

I hope this is helpful,

Catarina

Catarina Mar 10, 2020