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?

Saying that multiple choice questions are m, the equation is:
18m+19=15m+31
subtract 19 from both sides to get:
18m=15m+12
subtract 15m from both sides to get:
3m=12
divide by three to get the answer:
m=4
Each multiple choice question is worth 4 points