On a certain hot summer's day, 538 people used the public swimming pool. The daily prices are $1.75 for children and $2.25 for adults. The receipts for admission totaled $1125.50. How many children and how many adults swam at public pool that day?

The number of children was 170 and adults was 368.

Step-by-step explanation:

To clarify we'll call children by 'c' and adults by 'a'. The amount of people in the pool should be the sum of adults and children, so:

a + c = 538

The receipts for the adimission should total the amount of tickets from children and adults multiplied by the price of each ticket, so:

1.75*c + 2.25*a = 1125.5

We now have two equations and two variables. Using the first equation we can isolate the 'a' variable and use it on the second equation to find an answer. We then have:

a + c = 538

a = 538 - c

Using it on the second equation:

1.75*c + 2.25 * (538-c) = 1125.5

1.75*c + 1210.5 - 2.25*c = 1125.5

1.75*c - 2.25*c = 1125.5 - 1210.5

-0.5*c = - 85

c = - 85 / (-0.5) = 170

Using this value on the first equation:

a = 538 - 170 = 368

There were 170 children and 368 adults that swam at the public pool that day

Step-by-step explanation:

In this question, we are tasked with calculating the number of children and the number of adults that swam at a public pool on a particular day.

We proceed as follows:

Firstly, since we do not know their numbers, we can assign variables at this particular time. Let the number of children that swam be c while the number of adults that swam be a.

We had a total of 538 people that swam that day. This means when we add both numbers, total should be 538.

Mathematically:

a + c = 538 ... i

Now let's take a look at the finances. Price for children is $1.75 per child. Total amount realized from selling children's tickets that day is $1.75c. Price for adults is $2.25. Total amount realized from selling adults' tickets is $2.25a. Addition of both totaled $1125.50

Mathematically this means;

$1.75c + $2.25a = $1125.50 ... ii

This give a second equation we can solve together with the first.

From the first equation, we can rewrite that a = 538-c

We substitute this into the second equation:

1.75c + 2.25 (538-c) = 1125.5

1.75c + 1210.5 - 2.25c = 1125.5

2.25c-1.75c = 1210.5-1125.5

0.5c = 85

c = 85/0.5 = 170

From a = 538-c

a = 538-170 = 368

Hence, there were a total of 170 children and 368 adults that swam at the public pool on that day