on a certain hot summers day, 148 people used the public swimming pool. The daily prices are $1.75 for children and $2.50 for adults. The receipts for admission totaled $320.50. How many children and how many adults swam at the public pool that day?

66 children and 82 adults swam at the public pool that day.

Explanation:

Let x = the number of children
Let y = the number of adults

We can create two equations to represent this problem:

x + y = 148
1.75x + 2.50y = 320.50

There are multiple ways to solve this algebraically, but I think the easiest is rearranging the first equation and substituting it into the other equation and solving.

x + y = 148
becomes
x = 148 - y
^^^Note: the variable you arrange to solve for first doesn’t matter

Let’s plug this value for x into the second equation and solve.

1.75x + 2.50y = 320.50
1.75(148 - y) + 2.50y = 320.50
259 - 1.75y + 2.50y = 320.50
259 + 0.75y = 320.50
0.75y = 61.5
y = 82

Now that we’ve found one variable, we can plug this value into either one of the original equations to find the other variable.

x + y = 148
x + 82 = 148
x = 66

nd, we’ve found the answer! Now, to check, plug your variable values back into both equations to make sure they work.

x + y = 148
66 + 82 = 148
148 = 148

1.75x + 2.50y = 320.50
1.75(66) + 2.50(82) = 320.50
115.5 + 205 = 320.50
320.50 = 320.50