Question

On a certain hot​ summer's day, 84 people used the public swimming pool. The daily prices are $1.50 for children and $2.50 for adults. The receipts for admission totaled $179.00. How many children and how many adults swam at the public pool that​ day

Answer 1

So, there were 31 children and 53 adults who swam at the public pool that day.

Explanation:

Let's use a system of equations to solve this problem.

Let C represent the number of children and A represent the number of adults who swam at the public pool.

We know that there were 84 people in total, so we can write the equation:

C + A = 84

We also know that the total receipts for admission were $179.00, and the price for children is $1.50 and for adults is $2.50, so we can write another equation for the total cost:

1.50C + 2.50A = 179.00

Now, we can solve this system of equations. Let's first solve the first equation for C:

C = 84 - A

Now, substitute this expression for C in the second equation:

1.50(84 - A) + 2.50A = 179.00

Now, distribute and simplify:

126 - 1.50A + 2.50A = 179.00

Combine like terms:

126 + A = 179.00

Subtract 126 from both sides:

A = 179.00 - 126

A = 53.00

Now that we know there were 53 adults, we can find the number of children by using the first equation:

C + 53 = 84

Subtract 53 from both sides:

C = 84 - 53

C = 31

So, there were 31 children and 53 adults who swam at the public pool that day.