A math test with 26 questions is worth 100 points. There are multiple choice questions that are worth 2 points each and fill in the blank questions that are worth 5 points each. How many of each type of question is there?
A: 16 multiple choice, 10 fill in the blank
B: 20 multiple choice, 6 fill in the blank
C: 10 multiple choice, 16 fill in the blank
D: 6 multiple choice, 20 fill in the blank
Let's break down the information given in each option:
A: 16 multiple choice, 10 fill in the blank
The multiple choice questions are worth 2 points each, so 16 x 2 = <<16*2=32>>32 points.
The fill in the blank questions are worth 5 points each, so 10 x 5 = <<10*5=50>>50 points.
The total points earned for this option is 32 + 50 = <<32+50=82>>82 points.
B: 20 multiple choice, 6 fill in the blank
The multiple choice questions are worth 2 points each, so 20 x 2 = <<20*2=40>>40 points.
The fill in the blank questions are worth 5 points each, so 6 x 5 = <<6*5=30>>30 points.
The total points earned for this option is 40 + 30 = <<40+30=70>>70 points.
C: 10 multiple choice, 16 fill in the blank
The multiple choice questions are worth 2 points each, so 10 x 2 = <<10*2=20>>20 points.
The fill in the blank questions are worth 5 points each, so 16 x 5 = <<16*5=80>>80 points.
The total points earned for this option is 20 + 80 = <<20+80=100>>100 points.
D: 6 multiple choice, 20 fill in the blank
The multiple choice questions are worth 2 points each, so 6 x 2 = <<6*2=12>>12 points.
The fill in the blank questions are worth 5 points each, so 20 x 5 = <<20*5=100>>100 points.
The total points earned for this option is 12 + 100 = <<12+100=112>>112 points.
Only option C: 10 multiple choice, 16 fill in the blank, results in a total of 100 points, so the answer is C.