SOLUTION: University Theatre sold 493 tickets for a play. Tickets cost $23 per adult and $14 per senior citizen. If total receipts were $8270, how many senior citizen tickets were sold? C

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Question 540652: University Theatre sold 493 tickets for a play. Tickets cost $23 per adult and $14 per senior citizen. If total receipts were $8270, how many senior citizen tickets were sold?
Can you please show me step by step so i know how to solve it?
Thanks
Answer by Mathpassionate(25) About Me  (Show Source):
You can put this solution on YOUR website!

A = tickets sold for adults
C = tickets sold for Senior citizens

Information provided:

T = Total tickets sold
T = 493

23A = money got from selling tickets for adults
14C = money got from selling tickets for Seniors

23A + 14C = 8270

We know that "tickets sold for adults" + "tickets sold for Senior citizens" = "Total tickets sold"

That is:

A + C = T
A + C = 493

We work out "A" from the previous equation:

A = 493 - C

Now, substitute "A = 493 - C" into "23A + 14C = 8270"

23*(493-C) + 14C = 8270
11339 -23C + 14C = 8270
11339 -9C = 8270
11339 - 8270 = 9C
3069 = 9C
3069/9 = C
C = 341


The answer is that: 341 tickets for Senior Citizens were sold.


If we need the total tickets sold for Adults, just substitute "C = 341" into "A = 493 - C"

A = 493 - C
A = 493 - 341
A = 152


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