Question

Swimming Pool On a certain hot​ summer's day, 537 people used the public swimming pool. The daily prices are $1.75 for children and $2.50 for adults. The receipts for admission totaled $1050.00. How many children and how many adults swam at the public pool that​ day?

Answer 1

By setting up a system of linear equations and using the elimination method, we find that 391 children and 146 adults swam at the public pool that day.

Step-by-step explanation:

To solve the problem of how many children and adults swam at the public pool, we can set up a system of linear equations using the given information. Let's define 'c' as the number of children and 'a' as the number of adults. We have two equations:

• Equation 1 for the total number of people: c + a = 537
• Equation 2 for the total amount of money collected: 1.75c + 2.50a = 1050

We can solve this system using the substitution or elimination method. Assuming we use the elimination method, we multiply the first equation by 1.75 to eliminate 'c' when we subtract it from the second equation:

• 1.75c + 1.75a = 940.25
• 1.75c + 2.50a = 1050

Subtracting the first modified equation from the second, we get:

• 0.75a = 109.75

Dividing both sides by 0.75 gives us the number of adults:

• a = 146

We can then substitute the value of 'a' into the first equation to find 'c':

• c + 146 = 537
• c = 537 - 146
• c = 391

Therefore, 391 children and 146 adults swam at the public pool that day.