Answer
x = 15
y = 30
So...15 adults and 30 children attended the school play.
Step-by-step explanation
Part 1: Set up system of equations
We know that the sum of the number of children and the number of adults is equal to 45, so the first equation is...
{x + y = 45
(x = number of adults and y = number of children)
The second equation has to be focused more on the cost per person and the total profit...
{5x + 3y = 165
System of equations:
{x + y = 45
{5x + 3y = 165
Part 2: Solve for y
Get x by itself in the first equation and then substitute the right side of the resulting equation in for x in the second equation. Then solve for y.
x + y = 45
x + y - y = 45 - y
x = 45 - y
5x + 3y = 165
5(45 - y) + 3y = 165
225 - 5y + 3y = 165
225 - 2y = 165
-2y + 225 - 225 = 165 - 225
-2y = -60
-2y / -2 = -60 / -2
y = 30
Part 3: Solve for x
Substitute the value of y into the first equation and solve for x.
x + y = 45
x + 30 = 45
x + 30 - 30 = 45 - 30
x = 45 - 30
x = 15
I hope this helps!
