Question

On a certain hot summer day, 439 people used the public swimming pool. The daily prices are $1.75 for children and $2.50 for adults. The receipts for admission totaled $1021.00. How many children and how many adults swam at the public pool that day?

a) 200 children and 239 adults
b) 150 children and 289 adults
c) 275 children and 164 adults
d) 220 children and 219 adults

Answer 1

To determine the number of children and adults who swam at the public pool, set up a system of equations using the given information. Solve the system of equations to find the approximate number of children and adults. The answer is approximately 101 children and 338 adults. Hence the correct answer is option A

Step-by-step explanation:

To determine the number of children and adults who swam at the public pool that day, we can set up a system of equations to represent the given information. Let's assume there were x children and y adults. The total number of people is 439, so we have x + y = 439. The total receipts for admission is $1021, so we have 1.75x + 2.5y = 1021.

Multiplying the first equation by 1.75, we have 1.75x + 1.75y = 767.25. Subtracting this equation from the second equation, we get 2.5y - 1.75y = 1021 - 767.25, which simplifies to 0.75y = 253.75. Dividing both sides by 0.75, we find y = 338.33. This means there were approximately 338 adults.

Substituting this value into one of the original equations, we can solve for x. Using x + y = 439, we have x + 338.33 = 439. Subtracting 338.33 from both sides, we find x = 100.67. This means there were approximately 101 children.

Therefore, the answer is that there were approximately 101 children and 338 adults who swam at the public pool that day. So, the correct option is a) 200 children and 239 adults.