Question: Jasper and Corey have saved up a total of $78.00. Jasper [has] saved $6 more than twice as much as Corey. How much has Corey saved?
Answer: Let's look at the problem a bit. Jasper saved more than Corey. If we can think of a way to represent Corey's savings, we'll better understand how Jasper and Corey saved $78.
Let's translate the words a bit: "Jasper [has] saved $6 more than twice as much as Corey."
"More than" can be a "greater-than" problem (>) or an addition problem (+). We're looking at how Jasper and Corey together combined their money to save $78. This is an addition problem.
I don't know what Corey saved. Let's call that amount of money "x".
I don't know what Jasper saved, but it is $6 more than twice what Corey saved. "Twice what Corey saved." Doesn't that sound like two times what Corey saved? Doesn't that sound like two times "x"? Let's call that 2x. (Remember that this notation means "two times an unknown number.")
"$6 more than..." suggests that we need to add 6 to two times what Corey saved. "...add 6 to two times what Corey saved" sounds like we should do 6 + 2x.
Let's put everything together:
JASPER + COREY = 78
(6 + 2x) + x = 78. <---THIS is our model. Now let's get x by itself. Start by combining like terms (here, the x-terms).
6 + 2x + x = 78
6 + 3x = 78. Subtract 6 from both sides.
3x = 72. Now divide both sides by 3.
x = 24.
This means that Corey saved $24. Let's check this against our original story to make sure that we're right: Jasper and Corey together saved $78. Corey saved $24, and Jasper saved $6 more than twice what Corey made. Corey saved $24, and $24 times 2 is $48. Six dollars more than that is $54. So Jasper saved $54. Adding Jasper's $54 and Corey's $24 gets us $78. All is accounted for!
Corey saved $24.