On a certain hot summer's day, 294 people used the public swimming pool. The daily prices are for $1.75 children and for $2.25 adults. The receipts for admission totaled $635.50 How many children and how many adults swam at the public pool that day?

a = 242  adult and  c = 52 children

Step-by-step explanation:

Solving as a system of equations.

a = adult

c = children

The adult and the children equal 294 people

  a + c = 294

adult cost is 2.25 per adult

Total amount of adult is 2.25a because the number of adult are not given.

children cost is 1.75 per children

Total  amount children is 1.75c because the number of children  are not given

Total receipts $635.50.

a + c = 294                         multiply by -1.75           -1.75a - 1.75c = - 514.50

2.25a + 1.75c = 635.50     does not change           2.25a + 1.75c =  635.50

Add these equations together

-1.75a - 1.75c = - 514.50

2.25a + 1.75c =  635.50    

.50a              =   121.00

   a = 121.00/.50a

   a = 242  adult

a + c = 294

242 + c = 294

         c = 294 - 242

          c = 52 children

Check:    $2.25(242) + $1.75( 52) = $635 .50

              $544.50 + $91.00 =  $635.50

                   $635.50 = $635.50