Question 101245: admission for a college baseball game is $6 for box seats, $5 for the grandstand, and $3 for the bleachers. The total receipts for one evening were $9000. There were 100 more grandstand tickets sold than box seat tickets. Twice as many bleacher tickets were sold as box seat tickets. How many tickets of each type were sold?
Can anyone help me set this equation up?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let G represent the number of grandstand seats sold. Let B represent the number of box seats sold.
And let O represent the number of outfield bleacher seats sold.
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The problem tells you that the number of grandstand seats sold was 100 more than the number
of box seats sold. Therefore, you can write in equation form that:
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G = B + 100
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The problem also tells you that the number of outfield seats sold were twice the number of
box seats sold. In equation form this is:
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O = 2*B
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Since box seats were $6 each, the amount of money taken in for box seats is $6 times the
number of box seats sold. This means that the money from box seats is 6*B dollars.
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Since grandstand seats were $5 each the amount of money collected for grandstand seats is
$5 times the number of grandstand seats sold. But the number of grandstand seats sold is
B + 100. Therefore, the amount of money from grandstand seats is 5*(B + 100) dollars which
multiplies out to 5B + 500 dollars.
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Finally bleacher seats go for $3 each. So the amount of money collected for these outfield
seats is $3 times the number of outfield seats sold ... or 3*O. But O = 2*B. so the money
from outfield seats is 3*2*B or 6*B dollars.
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Now you can add all these three amounts of money and the total should be $9000.
So the
money equation is:
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6B + 5B + 500 + 6B = 9000
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Collect all the terms containing B on the left side and add them to make the equation
become
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17B + 500 = 9000
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Get rid of the 500 dollars on the left side by subtracting 500 from both sides to get:
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17B = 8500
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Solve for B by dividing both sides of this equation by 17 to get:
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B = 8500/17 = 500 box seats
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And since the number of grandstand seats sold was 100 more than the number of box seats,
then G = 500 + 100 = 600 grandstand seats
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Finally, the number of outfield seats sold was twice the number of box seats. So the number
of those seats was O = 2*B = 2*500 = 1000 bleacher seats.
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Check. 500 box seats were sold at $6 each for a total of $3000. 600 grandstand seats were
sold at $5 each for a total of $3000. And 1000 bleacher seats were sold at $3 each for
a total of $3,000. The total dollar amount taken in was $3,000 + $3,000 + $3,000 for a total
of $9000. It checks. Therefore, the seat count is correct.
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Hope this helps you to understand the problem.
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