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?

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.