You and your brother each start a child-care service. you spend $50 on supplies and plan to charge $10 per hour. your brother spends $30 on supplies and plans to charge $8 per hour. how many hours will each of you have to work to earn the same amount of money?

Okay, we'll split this up into two different equations.

Let X = hours worked, and Y = money earned

This is your equation : y = 10x - 50
This is your brothers : y = 8x - 30
Now, we know that you have to work to make the same amount of $$ (y value)

So set it equal to each other, **  10x-50 = 8x-30 **

10x-8x= -30+50
2x=20
x=10.

The answer is, you'll both have to work for 10 hours to make the same amount of money. That amount of money is $50. 

10  dollars an hour (10x) - the 50 dollars spent on supplies.
y=10x-50
8 dollars an hour (8x) - the 30 dollars spent on supplies.
z=8x-30

10x-50=8x-30
2x-50=8x-30
2x=20
x=10

It will take them 10 hours to earn the same amount of money.

Hope this helps :)