Question 81632: Help please!! I am stumped, any help would be greatly appreciated. Thank You
Adult tickets for a play cost $9 and child tickets cost $8. If there were 23 people at a performance and the theater collected $193 from ticket sales, how many children attended the play?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! There are two unknowns in this problem ... the number of adults and the number of children
that attend a play. This is a clue that you will need two equations to solve this problem.
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As a start, let A represent the number of adults and C represent the number of children.
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The problem tells you that 23 people attend the performance. This tells you that if you
add the number of adults and the number of children that attend, you should get an answer of 23.
In equation form this becomes:
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A + C = 23
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This is the first of the two equations.
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Next you can determine the amount of money taken in from adult tickets and also from children's
tickets. Since adult tickets are $9 each, the amount of money taken in from the sale of
adult tickets is $9 times the number of adults that attend or 9*A. Similarly, since
children's tickets are $8 each, the amount of money from the sale of children's tickets is
$8 times the number of children that attend or 8*C. The problem tells you that the total
amount from the sale of tickets is $193. In equation form this becomes:
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9*A + 8*C = 193
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This is the second equation that we need.
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The equations can be solved by substitution. Since the problem asks for the number of
children that attend the play, it would help if the second equation were converted so
that it contained only the variable C. You can do that by solving the first equation
for A in terms of C. Start with the first equation:
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A + C = 23
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Subtract C from both sides to get:
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A = 23 - C
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Then in the second equation you can substitute 23 - C for A. If you do that the second
equation becomes:
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9*(23 - C) + 8*C = 193
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Do the distributed multiplication on the left side to get:
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207 - 9*C + 8*C = 193
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On the left side combine the two terms that contain C and the equation becomes:
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207 - C = 193
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Now subtract 207 from both sides so that only the term involving C remains on the left
side. The subtraction of 207 from both sides results in:
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- C = 193 - 207 = - 14
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Finally, multiply both sides by -1 to eliminate the negative signs:
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C = 14
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So 14 children attend. (This means that of the 23 that attend 14 are children and the
remaining 9 are adults.)
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As a check, at $8 each for the 14 children's tickets, 8*14 equals $112 is taken in from
the sales of children's tickets. And at $9 each for the 9 adults that attend, the income
from the sale of adult tickets is 9*9 = $81. Therefore, the total income from the sale
of tickets is $112 + $81 = $193. That is exactly what it is supposed to be, so our answer
checks out. 14 children attend the play.
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Hope this helps you to understand the problem ... and how to get and solve the pair of
equations that is needed.
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