Question

art 1 of 2 Question content area top Part 1 Swimming Pool, On a certain hot​ summer's day, people used the public swimming pool. The daily prices are $1.25 for children and $2.25 for adults. The receipts for admission totaled $294.75. How many children and how many adults swam at the public pool that​ day?

Answer 1

Explanation:

x = number of children

y = number of adults

1.25x + 2.25y = 294.75

this has many different solutions.

we would need a total number of persons in the pool in order to solve that to a single solution.

so, it could be 131 adults and 0 children.

for every reduction of 5 adults we can add 9 children and keep the same total

so, it could be 126 adults and 9 children

121 adults and 18 children

116 adults and 27 children

...

1 adult and 234 children

how did I get to the 5 to 9 ratio ?

1.25 is 5/4.

2.25 is 9/4

so, I was looking for the smallest common multiple of 5 and 9. which is 45 or 5×9. there is no simpler ratio between them.

so, the ticket price of 9 children is the same as the ticket price of 5 adults.

in order to keep the total of $294.75, when I reduce the number of adults, I have to compensate by adding children with the same amount of ticket prices.

this does not charge the fact that your teacher gave you an incomplete problem to solve.

but maybe your teacher wanted you to discover this problem.