Question

On a certain hot​ summer's day, 288 people used the public swimming pool. The daily prices are $ 1.75 for children and $ 2.25 for adults. The receipts for admission totaled $ 571.50 .  How many children and how many adults swam at the public pool that​ day?

Answer 1

153 children, 135 adults

Explanation:

Let a represent the number of children

Let b represent the number of adults

a+b=288------equation 1

Since the daily price for children is $1.75 and the price for adults is $2.25. Then equation 2 can be expressed as

1.75a+2.25b=571.50-----equation 2

From equation 1

a+b=288

a=288-b

Substitute (288-b) for a in equation 2

1.75(288-b) +2.25b=571.50

504-1.75b+2.25b=571.50

Collect the like terms

-1.75b+2.25b= 571.50-504

0.5b=67.5

Divide both sides by the coefficient of b which is 0.5

0.5b/0.5=67.5/0.5

b= 135

Substitute 135 for b in equation 1

a+b=288

a+135=288

a=288-135

a= 153

Hence 153 children and 135 adults swam at the pool