On a certain hot summers day 284 people use the public swimming pool the daily prices are $1.50 for children and two dollars for adults their seats for admission total of $467 how many children and how many adult swim at the public pool that day

c = 202 children use the pool, and 284 - 202, or 82 adults.

Step-by-step explanation:

Represent the number of children by c and the number of adults by a.

There are a total of 284 people using the pool, so c + a = 284.

Admission fees are $1.50/child and $2.00/adult.  $1.50c is the amount taken in through ticket sales for c children;  $2.00a for adults.

Then total ticket sales are ($1.50/child)c + ($2.00/adult)a = $467.

Going back to c + a = 284, a = 284 - c, and so the above equation becomes

($1.50/child)c + ($2.00/adult)(284 - c) = $467

After simplifying this equation in c, we get:

1.50c + 568 - 2c = 467, or

101 = 0.5c.  Thus, c = 202 children use the pool, and 284 - 202, or 82 adults.