Question

Swimming Pool On a certain hot​ summer's day, 508 people used the public swimming pool. The daily prices are $ 1.75 for children and $ 2.25 for adults. The receipts for admission totaled $ 1083.00. How many children and how many adults swam?

Answer 1

120 children and 388 adults bought tickets for the swimming pool

Explanation:

Create two simultanous equations:

Let c stand for the number of children that bought a ticket, and a stand for the number of adults that bought a ticket, you get your first equation, being
`c+a = 508`

then, you now create a second equation for the prices of the tickets.
(price of childrens tickets)(number of children that swam)+(price of adults tickets)(number of adults that swam) = total money collected

so:
`1.75c + 2.25a = 1083.00`
now we still know, that `a=508-c`
so we can substitute it into the second formula
`1.75c + 2.25(508-c) = 1083`
now its just simple algebra
`1.75c + 1143 - 2.25 c = 1083`
`60 = 0.5c` so: `c=120`

now we know, that 120 children went to the swimming pool.
and we still have the formula from before:
`a = 508 - c` so `a = 388`