Hi, Gina--

The Problem:
Your brother earned $8 less than you. If you both earned $70, how much did each of you earn?

A Solution:
Let x be the amount of money you earned.

Since your brother earned $8 less, an expression for his earnings is x-8.

We know that together you and your brother earned $70.
[the amount you earned] + [the amount your brother earned] = [$70]
In algebra, we can write this relationship as
x + x-8 = 70

Now we solve this equation for x. Combine the x terms: x+x=2x.
2x - 8 = 70

Add 8 to both sides of the equation to get 2x by itself on the left hand side.
2x - 8 + 8 = 70 + 8

Combine the like terms: -8+8 =0 and 70+8=78.
2x = 78

Divide both sides of the equation by 2 to isolate the variable.
2x/2 = 78/2

Simplify both sides: 2x/2=x and 78/2=39
x = 39

In the context of this problem, x=39 means that you earned $39. Your bother earned $8 less, so he
earned $31 because 39-8=31.

We need to check that these numbers add up to a total of $70. Your $39 and your brother's $31 
add up to $70 because 39+31=70.

That's it. Please email me if you have questions or comments about the solution. I'd appreciate your
feedback. (It will make me a better "explainer.")

Ms.Figgy
math.in.the.vortex@gmail.com