University theater sold 491 tickets for a play. Tickets cost $25 per adult and $13 per senior citizen. If total receipts were $8195, how many senior citizen tickets were sold?

Answer 1

Let x = # of adults, and y = # of senior citizens...

Create two equations

x + y = 491 Equation 1

25x + 13 y = 8,195 Equation 2

Solve by method of substitution by rearranging equation 1 to be x = 491 - y.

As we have equation 1 in the form x = to something, substitute x into Equation 2.

23(491 - y) + 13y = 8195. Expand 2(491-y)

12,275 - 25y + 13y = 8195. Combine like terms

12,275 - 12y = 8195 Subtract 12,275 on both sides

-12y = -4080. Divide both sides by -12

y = 340

Using y = 340, substitute this into Equation 1 (x + y = 491) to solve for X

x + 340 = 491. Subtract 340 on both sides

x = 151

Therefore they sold 340 ticket to Senior Citizens and 151 ticket to Adults.

As a way to check, substitute answers into the equation 2

25(151) + 340 (13) : does this equal to 8195?

3775 + 4420 = 8195: the answer is yes.

Hope you can follow the steps. Let me know if you have additional questions or concerns!

Nathania

Answer 2