Answer:
<u>Admission prices are $3 per child and $4 per adult.</u>
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
<u>So, Admission prices are $3 per child and $4 per adult.</u>
