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At an amusement park, the cost of an adult's ticket is $22.50, and the cost of a child's ticket is $12.50. A group of 10 people purchased tickets for the amusement park, and paid a total of $155.00, excluding tax. How many children were in the group? How many adults were in the group?

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Answer:

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Step-by-step explanation:

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AnimalPost

Answer:

7 children and 3 adults

Step-by-step explanation:

We should set up a system of equations for this problem, so let's say that:

x represents the number of children

y represents the number of adults

We know there is a total of 10 people, so:

x + y = 10

We also know that each adult had to pay $22.50 and each child had to pay $12.50. Their total amount paid is $155.00, so:

12.50x + 22.50y = 155.00

Simplifying this a bit:

12.5x + 22.5y = 155

Now, we can use the substitution method to solve this system of equations:

x + y = 10

y = 10 - x

12.5x + 22.5y = 155

12.5x + 22.5 (10 - x) = 155

12.5x + 225 - 22.5x = 155

12.5x - 22.5x = 155 - 225

-10x = 155 - 225

-10x = -70

x = [tex]\frac{70}{10}[/tex]

x = 7 children

Now we substitute back into the system of equations:

x + y = 10

7 + y = 10

y = 10 - 7

y = 3 adults

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