Question

swimming pool on a certain hot summer’s day, 589 people used the public swimming pool. the daily prices are $1.50 for children and $2.00 for adults. the receipts for admission totaled $1013.00. how many children and how many adults swam at the public pool that day? there were \boxed{} children at the public pool.

Explanation:

Step1: Define Variables

Let \( c \) be the number of children and \( a \) be the number of adults. We know two equations: \( c + a = 589 \) (total people) and \( 1.50c + 2.00a = 1013 \) (total receipts).

Step2: Express \( a \) in Terms of \( c \)

From the first equation, \( a = 589 - c \).

Step3: Substitute into Receipts Equation

Substitute \( a = 589 - c \) into \( 1.50c + 2.00a = 1013 \):
\( 1.50c + 2.00(589 - c) = 1013 \)
Expand: \( 1.50c + 1178 - 2.00c = 1013 \)
Simplify: \( -0.50c + 1178 = 1013 \)
Subtract 1178: \( -0.50c = 1013 - 1178 = -165 \)

Step4: Solve for \( c \)

Divide by \(-0.50\): \( c = \frac{-165}{-0.50} = 330 \)

Answer:

330