What is the equation?

Question

You played a game with a regular round and a bonus round. During the regular round, a goal is worth 7 points. During the bonus round, a goal is worth 12 points. Your total was 105 points. If you scored 10 goals total, how many goals did you score in the first round?

Answer 1

let r be regular goals scored
let b be bonus goals scored

you have two equations:
r + b = 10 ...for # of goals
7r + 12b = 105 ...for points per goal

isolate one of variables so you can plug it into the other equation.
r = 10 - b (you can pick either r or b but you only need one)

now subtitute r and solve for b
7(10 - b) + 12b = 105
70 - 7b + 12b = 105
70 + 5b = 105
5b = 35
b = 7

now you know you scored 7 bonus goals, which means you scored 3 regular goals in the first round.

check:
7*12 = 84
3*7 = 21
84 + 21 = 105