On a certain hot summer's day, 744 people used the public swimming pool. The daily prices are $ 1.75 for children and $ 2.00 for adults. The receipts for admission totaled $ 1392.25 .How many children and how many adults swam at the public pool that day?

383 children and 361 adults

Step-by-step explanation:

Let's say there are a adults and c children. Since the total number of people was 744, we can write:

a + c = 744

We also know that children's prices are $1.75 per child and adults' prices are $2 per adult. Since the total is $1392.25, we can write:

1.75c + 2a = 1392.25

Now we have a system of linear equations:

a + c = 744

1.75c + 2a = 1392.25

Multiply the first equation by 2:

2 * (a + c = 744)  ⇒  2a + 2c = 1488

Now subtract the second equation from this one:

    2a + 2c = 1488

-    2a + 1.75c = 1392.25

    0a + 0.25c = 95.75

c = 383

Plug this in to find a:

a + c = 744

a + 383 = 744

a = 361

There were 383 children and 361 adults.

Lets use some variables:

x = number of adults

y = number of children

744 total people used the public swimming pool and the number adults and children are unknown, so, we can write an equation like:

x + y = 744

Since $2 are for adults, we can write that as 2x. Since $1.75 are for children, we can write that as 1.75y. Since the total price is $1,392.25, that's what the equation should equal. Equation:

2x + 1.75y = 1,392.25

Now, we have a system of equations.

~Rationalize equations

x + y = 744, 2x + 7/4y = 5569/4

~Isolate x for [ x + y = 744 ]

x + y - y = 744 - y

x = 744 - y

~Substitute with x

2(744 - y) + 7/4y = 5569/4

~Isolate y for [ 2(744 - y) + 7/4y = 5569/4 ]

2(744 - y) * 4 + 7/4y * 4 = 5569/4 * 4

8(744 - y) + 7y = 5569

5952 - 8y + 7y = 5569

5952 - y = 5569

5952 - 5952 - y = 5569 - 5952

-y = -383

-y/-1 = -383/-1

y = 383

~Substitute y with 383 in [ x = 744 - y ]

x = 744 - 383

x = 361

Therefore, there are 361 adults and 383 children.

Best of Luck!

hello from mrbilldoesmath!

answer:   x^2 + y^2 = 1024

discussion:

the equation of a circle with center (h,k) and radius "r" is

(x-h)^2 + (y-k)^2 = r^2.

in our case

(x-0)^2 + (y-0) ^2 = 32^2 = 1024

you,

mrb