Question

Emily went to the movie theater for her birthday. A mix of adults and children attended, making a total of 22 people. Each adult ticket was $9 and each child's ticket was $5.50. Is the total cost for the party was $125.5, then how many adults and how many children attended

Answer 1

Answer:

13 children and 9 adults if the total cost is $152.5

Step-by-step explanation:

Let x children and y adults

x + y = 22 (1)

5.5x + 9y = 125.5 (2)

y = 22 - x

5.5x + 9(22 - x) = 125.5

5.5x + 198 - 9x = 125.5

-3.5x = 125.5 - 198

-3.5x = -72.5

x = 20.7

y = 22 - x = 1.3

Which is not possible

If the total cost is $152.5

x + y = 22 (1)

5.5x + 9y = 152.5 (2)

y = 22 - x

5.5x + 9(22 - x) = 152.5

5.5x + 198 - 9x = 152.5

-3.5x = 152.5 - 198

-3.5x = -45.5

x = 13

y = 22 - 13 = 9

Answer 2

Using a system of equations, it is found that 1 adult and 21 children attended the party.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

• Variable x: Number of adults that attended the party.

• Variable y: Number of children that attended the party.

A mix of adults and children attended, making a total of 22 people, hence:

x + y = 22 -> y = 22 - x.

Each adult ticket was $9 and each child's ticket was $5.50, and the total cost of $125.5, hence:

9x + 5.5y = 125.5.

Since y = 22 - x:

9x + 5.5(22 - x) = 125.5

3.5x = 4.5

x = 4.5/3.5

x = 1(rounded).

y = 22 - 1 = 21.

Hence, 1 adult and 21 children attended the party.

More can be learned about a system of equations at https://brainly.com/question/24342899

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