SOLUTION: 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 adu
Question 1132020: 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? Found 2 solutions by Boreal, rothauserc:Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! 3A+2C=31
2A+3C=29
xA+6C=58 from the second row this would be 4A, doubling everything ANSWER
-6A-4C=-62
6A+9C=87
5C=25
C=$5
3A=21
A=$7
check the xA+6C and when A=$4 and C=$5, it is $58
You can put this solution on YOUR website! let a be the cost of a ticket for an adult and c be the cost for a child
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1) 3a +2c = 31
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2) 2a +3c = 29
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subtract equation 2 from equation 1
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a -c = 2
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3) a = c +2
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substitute for a in equation 1
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3(c+2) +2c = 31
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3c +6 +2c = 31
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5c = 25
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c = 5
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substitute for c in equation 3
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a = 5 +2 = 7
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let x be the number of adults in the group
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4) 7x +6(5) = 58
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7x +30 =58
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7x = 28
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x = 4
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There are 4 adults in the group
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check this answer with equation 4
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7(4) +6(5) = 58
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28 +30 = 58
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58 = 58
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answer checks
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Note the cost of an adult ticket is $7 and a child ticket is $5
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Check these cost values
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equation 1
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3(7) +2(5) = 31
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21 +10 = 31
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31 = 31
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equation 2
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2(7) +3(5) = 29
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14 +15 = 29
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29 = 29
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answers check
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