Question

On a certain hot summer's day, 528 people used the public swimming pool. The daily prices are $1.75 for children and $2.00 for adults. The

receipts for admission totaled $961.50. How many children and how many adults swam at the public pool that day?
There were
There were
children at the public pool.
adults at the public pool.

Answer 1

378 children; 150 adults

Explanation:

We can determine the number of children and adults at the pool using a system of equations, where

• C represents the number of children at the pool.
• and A represents the number of adults at the pool.

First equation:

We know that the sum of the number of adults and children at the pool equals the total number of people at the pool:

number of adults + number of children = total number of people

Since there were 528 people at the pool, our first equation is given by:

C + A = 528

Second equation:

We also know that the sum of the revenues earned from the children and adults equals the total revenue:

(admission price * number of children) + (admission price * number of adults) = total revenue.

Since the total revenue was $961.50, our second equation is given by:

1.75C + 2.00A = 961.50

Method to solve: Substitution:
First, we can isolate A in the first equation.

(C + A = 528) - C

A = -C + 528

Solving for C (the number of children):

Now we can solve for C (The number of children) by substituting -C + 528 for A in the second equation (1.75C + 2.00A = 961.50):

1.75C + 2.00(-C + 528) = 961.50

1.75C - 2.00C + 1056 = 961.50

(-0.25C + 1056 = 961.50) - 1056

(-0.25C = -94.5) / -0.25

C = 378

Thus, there were 378 children at the public pool that day.

Solving for A (the number of adults):

Finally, we can solve for A (the number of adults) by plugging in 378 for C in he first equation (C + A = 528):

(378 + A = 528) - 378

A = 150

Thus, there were 150 adults at the public pool that day.