University Theater sold 556 tickets for a play. Tickets cost $22 per adultand $12 per senior citizen. If total receipts were $8492, how many seniorcitizen tickets were sold?

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22-02-2017
Mathematics

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University Theater sold 556 tickets for a play. Tickets cost $22 per adultand $12 per senior citizen. If total receipts were $8492, how many seniorcitizen tickets were sold?

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corajune99 corajune99 · Answer 1 · 2017-02-22T21:30:43+01:00

To find the answer, set up a system of equations.

Let x=adult tickets and y=senior citizen tickets.

x+y=556
22x+12y=8492

Change the first equation to make it easy to combine with the second equation.

y=556-x

Now substitute (556-x) for y in the second equation.

22x+12(556-x)=8492

Simplify and combine like terms.

22x+6672-12x=8492
10x=1820
x=182

182 adult tickets were sold, so to solve for the number of senior citizen tickets sold, subtract 182 from 556.

556-182=374

374 senior citizen tickets were sold.