Question 1131073: On weekdays, a movie theater charges different rates for adults and
children. If 3 adults and 2 children go for a movie on a weekday, the total
cost of the tickets is $31. If 2 adults and 3 children go on a weekday, the
total cost of the tickets is $29. If a group of adults and 6 children go to the movie theater on a weekday and pay $58 for tickets, how many adults are
in this group?
A. 4
B. 5
C. 7
D. 8
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! On weekdays, a movie theater charges different rates for adults and
children.
If 3 adults and 2 children go for a movie on a weekday, the total
cost of the tickets is $31.
If 2 adults and 3 children go on a weekday, the
total cost of the tickets is $29.
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Equations:
3a + 2c = 31
2a + 3c = 29
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Modify and solve for "a"::
9a + 6c = 3*31
4a + 6c = 2*29
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Subtract and solve for "a":
5a = 93-58
5a = 35
a = 7 (price of an adult ticket)
Solve for "c"::
3a + 2c = 31
3*7+2c = 31
2c = 10
c = 5 (price of a child's ticket)
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If a group of adults and 6 children go to the movie theater on a weekday and pay $58 for tickets, how many adults are
in this group?
A + 6c = 58
A + 6*5 = 58
A = 28 dollars (cost for the group of adults)
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Ans: # of adults = 28/7 = 4
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Cheers,
Stan H.
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A. 4
B. 5
C. 7
D. 8
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