public swimming pool question

Question

On a certain hot​ summer's day, 254 people used the public swimming pool. The daily prices are $1.75 for children and $2.50 for adults. The admission receipts totaled $612.50 How many children and how many adults swam at the public pool that​ day?

Answer 1

Hi Emma,

First we must recognize that is a linear system of equations, so we can set them up as such:

1.75x + 2.50y = 612.50

x + y = 254

Our goal is to solve for either x or y, and then substitute that value to get the other value. We can do this either through the substitution or elimination method. Here, I will do it via the substitution method:

x + y = 254 --> x = 254 - y

1.75(254 - y) + 2.50y = 612.50

444.5 - 1.75y + 2.50y = 612.50

444.5 + 0.50y = 612.50

0.75y = 168

y = 168 / 0.75 = 224 adults

Now we plug in this y value and solve for x (number of children):

x + (224) = 254

x = 30 children

Therefore, 224 adults and 30 children swam at the public pool that day.