Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

The manager at a community pool is looking over receipts. On a certain Monday, the pool had 10 children and 37 adults, which brought in $178. That same week on Tuesday, 15 children and 23 adults came to the pool, which brought in $137. What are the admission prices for children and adults?

Admission prices are $ per child and $ per adult.

Admission prices are $3 per child and $4 per adult.

Step-by-step explanation:

Let the admission prices for children = x and for adults = y

When the pool had 10 children and 37 adults, which brought in $178

10x + 37y = 178 ⇒(1)

When the pool had 15 children and 23 adults, which brought in $137

15x + 23y = 137 ⇒(2)

Multiplying eq.(1) by 3  ⇒ 30x + 111y = 534 ⇒(3)

Multiplying eq.(2) by 2 ⇒ 30x + 46y = 274 ⇒(4)

Find eq.(3) - eq.(4)

∴ 111y - 46y = 534 - 274

∴ 65y = 260

∴ y = 260/65 = 4

By substitution with y at eq.(1)

10x + 37 * 4 = 178  ⇒ solve for x

10x = 178 - 37*4 = 30

∴ x = 30/10 = 3

So, Admission prices are $3 per child and $4 per adult.

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answer: sensy

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