a math test with 26 questions is worth 100points there are multiple choice questions that are worth 2 points each fill in the blank questions that are worth 5 points each how many of each type of question is there
Let's assume the number of multiple-choice questions is m, and the number of fill in the blank questions is f.
From the given information, we can form two equations:
m + f = 26 (Equation 1, since there are 26 questions in total)
2m + 5f = 100 (Equation 2, as each multiple-choice question is worth 2 points and each fill in the blank question is worth 5 points)
To solve these equations, we can multiply Equation 1 by 2 and subtract it from Equation 2:
2(26 - f) + 5f = 100
52 - 2f + 5f = 100
3f = 48
f = 16
Substitute this value of f back into Equation 1 to solve for m:
m + 16 = 26
m = 10
Therefore, there are 10 multiple-choice questions and 16 fill in the blank questions.