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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.

User Morissette
by
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1 Answer

6 votes

Answer:

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.

User Hett
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