Systems of Linear Equations Unit Test

Question

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Question
The Kesling Middle School PTA is planning a carnival to raise money for the school’s art department. They estimate that the event will be very popular and that they will have 500 people attend. They plan to charge adults $10 and children $5 for admission. The PTA wants to earn $3,500 from admission charges. How many adults and how many children need to attend for the PTA to reach their goal of $3,500?(1 point)
adults;
children

Answer 1

Let:
A = number of adults
C = number of children

From the given information, we can create a system of equations:

A + C = 500 (total number of people attending)
10A + 5C = 3500 (amount earned from admission charges)

Now, let's solve the system of equations.

From the first equation, we can express A in terms of C as A = 500 - C.

Substitute this expression for A into the second equation:

10(500 - C) + 5C = 3500
5000 - 10C + 5C = 3500
5000 - 5C = 3500
-5C = -1500
C = 300

Now that we have found the number of children attending, we can find the number of adults:

A = 500 - C
A = 500 - 300
A = 200

Therefore, the PTA needs 200 adults and 300 children to attend in order to reach their goal of $3,500.