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A local dinner theater sells adult tickets for $105 each and children’s tickets for $60 each.  For a certain show the theater sells 84 tickets for a total of $7155. Write a system of equations that models this problem and then show all the steps to solve your system of equations using linear combination.

 Jan 23, 2020
 #1
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Since know the number of tickets is 84, the number of children's tickets can expressed as the total number of tickets minus the adult tickets or 84-x where x is the number of adult tickets. Then we have the following equation:
 

105*x+60(84-x)=7155

Factor out the equation to get

105x+60*84-60x=7155

Next up we get x alone on the left side of the equation and get

105x-60x=7155-60*84

45x=7155-5040

45x=2115

x=2115/45

x=47

y=84-47

y=37

 

You can check this by putting the values into the equation: 47*105+60*37

 

Cheers

 Jan 23, 2020
edited by danne9000  Jan 23, 2020
 #2
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Thanks so much! 

Guest Jan 23, 2020

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