Answer:
1. 5
2. 3 adult tickets; 2 child tickets
3. See below
Step-by-step explanation:
1.
2 adult tickets cost 2 × $12 = $24
Subtract $24 from $64:
$64 - $24 = $40
Divide $40 by $8:
$40 ÷ $8 = 5
Answer: 5 child tickets
2.
x = number of adult tickets
y = number of child tickets
The total number of tickets is 5, so the first equation is:
x + y = 5
The cost of x adult tickets is 12x. The cost of y child tickets is 8y. The total cost is 12x + 8y. We are told the total cost is $52. The second equation is:
12x + 8y = 52
The system of equation is:
x + y = 5
12x + 8y = 52
Let's solve it by substitution.
Solve the first equation for x.
x = 5 - y
Now we substitute x in the second equation by 5 - y.
12(5 - y) + 8y = 52
Distribute:
60 - 12y + 8y = 52
Combine like terms on the left side:
-4y + 60 = 52
Subtract 60 from both sides:
-4y = -8
Divide both sides by 4.
y = 2
Substitute y = 2 in the first original equation and solve for x.
x + y = 5
x + 2 = 5
x = 3
Answer: 3 adult tickets; 2 child tickets
3.
The customer's claim is incorrect. His sum is $71. 71 is an odd number. Since all ticket prices are even numbers, it is impossible to add only even numbers and get an odd sum. A sum of several amounts of 12 and several amounts of 8 can never equal 71.
We can also show his claim is false using a system of equations.
x + y = 7
12x + 8y = 71
Use substitution.
x = 7 - y
12(7 - y) + 8y = 71
84 - 12y + 8y = 71
84 - 4y = 71
-4y = -13
y = 3.25
This means 3.25 child tickets. The problem states that tickets can be purchased only in whole numbers, so 3.25 tickets cannot be purchased, so the customer's claim is false.
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