
Aneesh C. answered 01/17/21
Adept Math/Statistics/SAS Tutor: M.S Public Health, B.S Biology
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.