Question

Help with this word problem!

Answer 1

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!