On a certain hot summers day, 672 people used the public swimming pool. The daily prices are $1.50 for children and 2.50 for adults. The receipts for admission totaled $1289.00. How many children and how many adults swam at the public pool that day?

Adults = 281
Children = 391

We have two equations: number of people and money. I’ll use a for adults, c for children.

a + c = 672
2.5a + 1.5c = 1289

First we’ll solve for number of adults in terms of c
a = 672-c

Then drop that expression into the second equation to solve for a numerical value for c

2.5(672-c) + 1.5c = 1289
1680 - 2.5c + 1.5c = 1289
-c = -391
c = 391

Now put that into the first equation to get a numerical value for a

a + 391 = 672
a = 281

Checking the math:
2.5(281) + 1.5(391)
= 702.5 + 586.5
= $1289