SOLUTION: University theater sold 515 tickets for a play. Tickets cost $20 per adult and $13 per senior citizen. If total receipts were $7822, how many senior tickets were sold?
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Question 684844: University theater sold 515 tickets for a play. Tickets cost $20 per adult and $13 per senior citizen. If total receipts were $7822, how many senior tickets were sold?
Found 2 solutions by mananth, MatrixWoman:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
x= number of adult tickets
y= number of senior citizen tickets
Total tickets sold
1 x + 1 y = 515 .............1
20 x + 13 y = 7822 .............2
Eliminate y
multiply (1)by -13
Multiply (2) by 1
-13 x -13 y = -6695
20 x + 13 y = 7822
Add the two equations
7 x = 1127
/ 7
x = 161
plug value of x in (1)
1 x + 1 y = 515
161 + y = 515
y = 515 -161
y = 354
y = 354
x= 161 number of adult tickets
y= 354 number of senior citizen tickets
m.ananth@hotmail.ca
Answer by MatrixWoman(6) (Show Source): You can put this solution on YOUR website!
20x+13y=7822
x+y=515
x is the number of adults that went to the play and y is the number of seniors that went to the play.
Take your second equation and solve for y:
y=515-x
then substitute what your found for y into the first equation's y:
20x+13(515-x)=7822
20x+6695-13x=7822
7x+6695=7822
7x=1127
x=161
Then plug in 161 for x into your second equation to find y:
161+y=515
y=354
Then to double check plug in 354 for y in your first equation to find x:
20x+13(354)=7822
20x+4602=7822
20x=3220
x=161 (It worked!!)
161 adults went, and 354 seniors went to the play.
I hope this helps :)
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