Question 101245
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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