Question

On a certain hot​ summer's day, 350 people used the public swimming pool. The daily prices are 1.25 for children and 2.50 for adults. The receipts for admission totaled 627.50 How many children and how many adults swam at the public pool that​ day?

Answer 1

198 children, 152 adults

Explanation:

So this problem can be broken down into an equation system with 2 equations.
Let's use variable x for number of children and y for number of adults.
You are given, that 350 people in total used the pool on this certain day.
This gives you the first equation:
x + y = 350

Then you are given the totaled admission of 627.50. When each child paid 1.25 and each adult paid 2.50, this gives you the second equation:
1.25*x + 2.50*y = 627.50

To get the value of both x and y, first solve one equation for x;
x + y = 350
x = 350 - y

and then put this value into the other equation:
1.25*x + 2.5*y = 627.5
1.25*(350-y) + 2.5*y = 627.5

and then you solve for y:
437.5 -1.25*y + 2.5*y = 627.5
437.5 + 1.25*y = 627.5
1.25*y = 190
y = 152

so 152 adults used the pool this day.
Then you put this value for y into any of your equations and solve for x:
x + y = 350
x + 152 = 350
x = 350 - 152
x = 198

so 198 children used the pool this day.