Answer:
The correct answer is D. 12 adult tickets, 4 child tickets
Step-by-step explanation:
Number of people paying for a ticket to the museum = 16
Cost of adult ticket = US$ 4
Cost of child ticket = US$ 2
Total paid by the 16 people = US$ 56
Number of adults = x
Number of children = 16 - x
This is the equation to find out how many adults and how many children were in the group:
4x + 2 (16 - x) = 56 (Number of adults * cost of adult ticket plus Number of children * cost of children ticket equals to the total paid)
4x + 32 - 2x = 56
2x = 56 -32
2x = 24
x = 12 (Dividing by 2 at both sides of the equation)
12 adult tickets were bought, so 4 child tickets were also bought. Let's check it :
12 adult tickets cost US$ 48 and 4 child tickets cost US$ 8
48 + 8 = 56
The correct answer is 12 adult tickets, 4 child tickets, that is D
Therefore, to determine the number of children, we have to subtract the number of people that bought the tickets from the number of children; therefore, the number of children can be expressed as
Number of children = 16 – x
We have determine the number of adult and children by multiplying the number of adult with the cost of adult ticket plus the number of children multiply with the cost of children ticket and equals to the total tickets bought by the 16 people.
Therefore, it can be expressed as:
[tex]4x[/tex] + [tex]2(16-x)[/tex] = [tex]56[/tex]
[tex]4x[/tex] + (2 x 16) – (2 x X) = [tex]56[/tex]
[tex]4x[/tex] + [tex]32[/tex] – [tex]2x[/tex] = [tex]56[/tex]
4x – 2x = [tex]56[/tex] – [tex]32[/tex]
2x = [tex]24[/tex]
X = [tex]\frac{24}{2}[/tex]
X = [tex]12[/tex]
This implies that 12 adults’ tickets were bought and 4 child tickets were brought as well.
Therefore if 12 adults ticket cost $48, then the remaining ticket would be for the children.
That is, 56 – 48 = 8
Thus, 12 adults ticket cost $48 and 4 child ticket cost $8
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