SOLUTION: Please help! Can you give me a step by step solution? "A community theater sold 900 tickets to a play. Floor seats cost 12$ each, and balcony seats cost 10$. The total receipt

Question 98560This question is from textbook Beginning Algebra
: Please help! Can you give me a step by step solution?

"A community theater sold 900 tickets to a play. Floor seats cost 12$ each, and balcony seats cost 10$. The total receipts were 9780$. How many of each type of ticket were sold?"

Thank you very much! This question is from textbook Beginning Algebra

Found 2 solutions by stanbon, checkley71:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A community theater sold 900 tickets to a play. Floor seats cost 12$ each, and balcony seats cost 10$. The total receipts were 9780$. How many of each type of ticket were sold
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Let # of $12 tickets be "x" ; Value of these is 12x dollars
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# of $10 tickets is "900-x" ; Value of these is 10(900-x)=9000-10x dollars
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EQUATION:
value + value = $9780
12x + 9000-10x = 9780
2x = 780
x = 390 (# of $12 tickets)
900-x = 510 (# of $10 tickets)
==============
Cheers,
Stan H.
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
F+B=900 OR F=900-B
12F+10B=9780 NOW REPLACE F IN THIS EQUATION BY (900-B) & SOLVE FOR F.
12(900-B)+10B=9780
10800-12B+10B=9780
-2B=9780-10800
-2B=-1020
B=-1020/-2
B=510 BALCONY TICKETS WERE SOLD.
900-510=390 FLOOR TICKETS WERE SOLD.
PROOF
12*390+10*510=9780
4680+5100=9780
9780=9780
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