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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?

 Mar 10, 2020
 #1
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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

 Mar 10, 2020
 #2
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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 smiley

 Mar 10, 2020
edited by Catarina  Mar 10, 2020

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