Question 289790: Concert tickets cost $25 for the balcony and $40 for the floor. If the total amount collected was $10,000, how many of each tickets were sold? A total of 325 tickets were sold.
Answer by amnd(23)   (Show Source):
You can put this solution on YOUR website! Say that f = number of floor tickets sold and b = number of balcony tickets sold.
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The total amount of tickets sold is 325, which means that b + f = 325
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The total amount collected is $10000, which means that the amount of tickets sold multiplied by the amount it costs would be 25b + 40f = 10000, which can be simplified by a division of 5 to: 5b + 8f = 2000
The first equation can be multiplied by five, and the rest is just a matter of simple substitution:
5b + 8f = 2000 <- second equation
5b + 5f = 1625 <- first equation
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0 + 3f = 375
Since 3f = 375, f = 125
The amount of balcony tickets sold (b) can be determined from b + f = 325, which means that b = 325 - f = 325 - 125, and b = 200
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