Answer: 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
Aaaand, 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
