Question 1132020
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
:
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
:
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
:
3(7) +2(5) = 31
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21 +10 = 31
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31 = 31
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equation 2
:
2(7) +3(5) = 29
:
14 +15 = 29 
:
29 = 29
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answers check
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