Question

On a certain hot​ summer's day, 298 people used the public swimming pool. The daily prices are $1.50 for children and $2.00 for adults. The receipts for admission totaled $478.50. How many children and how many adults swam at the public pool that​ day? There were nothing children at the public pool. There were nothing adults at the public pool.

Answer 1

There were 63 adults and 235 children at the public swimming pool.

Explanation:

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

• C represents the number of children,
• and A represents the number of adults.

First equation:

Since there were 298 people at the pool, our first equation is given by:

C + A = 298

Second equation:

We know that the revenue earned from the children and adult admission fees equals the total revenue of $478.50:

(children admission price * quantity) + (adult admission price * quantity) = 478.50

Since the price for children was $1.50 and the price for adults was $2.00, our second equation is given by:

1.50C + 2.00A = 478.50

Method to solve: Elimination:

Multiplying the first equation by -1.50C will allow us to eliminate C since -1.50C + 1.50C = 0:

-1.50(C + A = 298)

-1.50C - 1.50A = -447

Solving for A:

Now we can add -1.50C - 1.50A = -447 to the second equation (i.e., 1.50C + 2.00A = 478.50) to eliminate C and solve for A:

-1.50C - 1.50A = -447

+

1.50C + 2.00A = 478.50

----------------------------------------------------------------------------------------------------------(-1.50C + 1.50C) + (-1.50A + 2.00A) = (-447 + 478.50)

(0.50A = 31.50) / 0.50

A = 63

Thus, there were 63 adults at the public swimming pool.

Solving for C:

Now we can solve for C by plugging in 63 for A in the first equation (i.e., C + A = 298):

(C + 63 = 298) - 63

C = 235

Thus, there were 235 children at the public swimming pool.