Question

Swimming Pool On a certain hot summer's day, 345 people used the public swimming pool. The daily prices are $1.50 for children and $2.50 for adults. The receipts for admission totaled $691.50. How many children and how many adults swam at the public pool that day?​

Answer 1

To solve the problem, set up a system of equations representing the number of children and adults swimming. Using substitution, solve for the variables and find the values of C (number of children) and A (number of adults). There were 171 children and 174 adults swimming at the public pool that day.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's define two variables: let's call the number of children swimming 'C' and the number of adults swimming 'A'. Since there were 345 people in total, we know that C + A = 345. Additionally, we know that the total cost of the children's tickets plus the total cost of the adults' tickets equals $691.50. So we can write the equation 1.5C + 2.5A = 691.50.

Now we can solve this system of equations using any method we prefer. In this case, let's use substitution.

From the first equation, we can solve for C: C = 345 - A. Substituting this into the second equation, we get:

1.5(345 - A) + 2.5A = 691.50

Expanding and simplifying, we get:

517.5 - 1.5A + 2.5A = 691.50

Combining like terms, we have:

517.5 + A = 691.50

Subtracting 517.5 from both sides, we get:

A = 174

Now we can substitute this value of A back into the first equation to find C:

C = 345 - 174 = 171

Therefore, there were 171 children and 174 adults swimming at the public pool that day.