SAT Math Question: Word Problem

Every week, Emily and Jacob each write one story for an online magazine. Emily is paid $200.00 plus 5% of the advertising revenue for her story. Jacob is paid $150.00 plus 10% of the advertising revenue for his story. If they both generated the same amount of advertising revenue, and received equal paychecks for the week, how much in dollars, was each paid?

Important points in this problem:
1) Set up the equations correctly! This includes getting the percents right, and defining your variables correctly.
2) Answer the question! Specifically, do NOT reply with how much advertising revenue there is.

Let E represent how much Emily earns.
Let J represent how much Jacob earns.
Let x represent how much advertising revenue each person earns.

E = 200 + 5% of x
J = 150 + 10% of x

Remember that 5% of x is just 0.05 * x, or x/20. Similar calcs for 10% of x. Simplifying, we get:

E = 200 + 0.05x
J = 150 + 0.1x

Now, the problem says they received equal paychecks. That means E = J. So we have:
200 + 0.05x = 150 + 0.1x

Move all x's to the right:
200 = 150 + 0.05x

Move all constants to the left:
50 = 0.05x

You have two choices that are really the same. You can divide by 0.05, or multiply by 20. Either way, you get:

50 * 20 = 0.05x * 20
1000 = 1x

So x = 1000. They each made $1,000, right?

CAREFUL! You have to answer the question of how much each was paid. So, plug x back in to get E and J:
E = 200 + 0.05 * 1000
E = 200 + 50
E = $250

J = 150 + 0.1 * 1000
J = 150 + 100
J = $250

This confirms our answer: when the advertising revenue is $1000, they EACH get paid the same amount, or $250.

Here's a fun shortcut: you might notice that Jacob gets twice as much from the advertising revenue than Emily does. So, let's define a new variable, y, that is equal to how much of the advertising revenue Emily gets. We can see that: