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

Answer by rothauserc(4718) (Show Source): 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
:
1) 3a +2c = 31
:
2) 2a +3c = 29
:
subtract equation 2 from equation 1
:
a -c = 2
:
3) a = c +2
:
substitute for a in equation 1
:
3(c+2) +2c = 31
:
3c +6 +2c = 31
:
5c = 25
:
c = 5
:
substitute for c in equation 3
:
a = 5 +2 = 7
:
let x be the number of adults in the group
:
4) 7x +6(5) = 58
:
7x +30 =58
:
7x = 28
:
x = 4
:
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There are 4 adults in the group
:
check this answer with equation 4
:
7(4) +6(5) = 58
:
28 +30 = 58
:
58 = 58
:
answer checks
:
Note the cost of an adult ticket is $7 and a child ticket is $5
:
Check these cost values
:
equation 1
:
3(7) +2(5) = 31
:
21 +10 = 31
:
31 = 31
:
equation 2
:
2(7) +3(5) = 29
:
14 +15 = 29
:
29 = 29
:
answers check
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