Question

Gretchen and Ezia received equal scores on a test made up of multiple choice questions and an essay. Gretchen got 18 multiple choice questions correct and received 19 points for her essay. Ezia got 15 multiple choice questions correct and received 31 points for her essay.

How many points was each multiple choice question worth?

Answer 1

Let's say a multiple choice's score is called x. Gretchen got 18x + 19 points, while Ezia got 15x + 31. We know they had the same score, so this equation is true:
\[18x + 19 = 15x + 31\]
We move the 19 to the 31 side and the 15x to the 18x side and solve for x. Do you know how to do that now or should I go over it?

Answer 2

keep going

Answer 3

Sorry, went out for the night. Here's the equation with the constants and variables on the same side:
\[18x-15x = 31 - 19\]
Subtract the numbers:
\[3x = 12\]
Divide both sides by 3.
\[x = 4\]
Magic! :)