SWIMMING POOL How many children and how many adults swam at the public pool that day?

Question

SWIMMING POOL On a hot summer's day, 393 people used the public swimming pool. The daily prices are $1.50 for children and $2.25 for adults. The receipts for admission totaled $809.25. How many children and how many adults swam at the public pool that day?

Answer 1

Let x=the number of children and y=the number of adults swam on the day. Then

1.5x+2.25y =809.25 ....(1)

x+ y = 393 ...(2)

From equation (2), we have x=393-y substitute x=393-y into equation (1), we have

1.5(393-y)+2.25y=809.25

combine the terms with y and combine all numbers to get

(2.25-1.5)y=809.25-1.5(393)=219.75

0.75y=219.75

y=219.75/.75=293

so x=393-y=393-293=100

Therefore, on the day, there ere 100 children and 293 adults swam.

Answer 2

This is a system of equations problem!

First, we will assign variables to children (c) and adults (a). We know that the total number of children and adults is 393 people, therefore our first equation is:

a + c = 393

Next, we will take the prices into account to create the next equation. Because the cost of an adult ticket is $2.25, price of adult tickets is the number of adults (a) multiplied by the price; for the children, it is the number of children (c) multiplied by $1.50, the price of a child ticket. The total number of tickets is $809.25, therefore the equation is:

(2.25)a + (1.5)c = 809.25

We now have two equations. To solve for the variables, we will manipulate the first equation to isolate a variable so that we can plug it into the second:

a + c = 393

a = 393 - c

Because (a = 393 - c), we can plug (393 - c) in to the second equation for a:

(2.25)a + (1.5)c = 809.25

(2.25)(393 - c) + (1.5)c = 809.25

884.25 - 2.25c + 1.5c = 809.25

-0.75c = -75

c = 100

To solve for the number of adults, we can plug this value of c back into either equation to get a:

a + c = 393

a + 100 = 393

a = 293

To check the answer, we can plug both of the values into one of the equations to ensure it checks out:

(2.25)a + (1.5)c = 809.25

(2.25)(293) + (1.5)(100) = 809.25

659.25 + 150 = 809.25

809.25 = 809.25!

It checks out!