Multiple choice questions were worth some points.
We don't know how many yet. That's what we're trying to find.
Call it ' M ' (for 'mystery number' or 'multiple-choice')
Francine got 34 multiple choice questions correct.
She got 34M points for them.
She got 14 more points for her essay.
Her total score was 34M + 14.
Cheryl got 30 multiple choice questions correct.
She got 30M points for them.
She got 22 more points for her essay.
Her total score was 30M + 22.
THEIR SCORES WERE EQUAL.
So 34M + 14 = 30M + 22
Subtract 14 from each side 34M = 30M + 8
Subtract 30M from each side: 4M = 8
Divide each side by 4 : M = 2
Each multiple choice question is worth 2 points. Exactly. 2.00000
Check:
Francine got 34 questions right . . . 68 points
plus 14 for her essay => total 82 .
Cheryl got 30 questions right . . . 60 points
plus 22 for her essay => total 82 . yay!
