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?
Responses
A 16 multiple choice, 10 fill in the blank16 multiple choice, 10 fill in the blank
B 20 multiple choice, 6 fill in the blank20 multiple choice, 6 fill in the blank
C 10 multiple choice, 16 fill in the blank10 multiple choice, 16 fill in the blank
D 6 multiple choice, 20 fill in the blank6 multiple choice, 20 fill in the blank
To solve this problem, let's assume the number of multiple choice questions as 'x' and the number of fill in the blank questions as 'y'.
According to the given information, the total number of questions is 26:
x + y = 26 ----(1)
The score for multiple choice questions is 2 points each, so the total score for multiple choice questions would be 2x.
The score for fill in the blank questions is 5 points each, so the total score for fill in the blank questions would be 5y.
The total score for the test is 100 points:
2x + 5y = 100 ----(2)
Now, we need to solve these two simultaneous equations to find the values of 'x' and 'y'.
By multiplying equation (1) by 2, we get:
2x + 2y = 52 ----(3)
Subtracting equation (3) from equation (2), we get:
(2x + 5y) - (2x + 2y) = 100 - 52
3y = 48
y = 48/3
y = 16
Substituting the value of 'y' in equation (1), we get:
x + 16 = 26
x = 26 - 16
x = 10
So, the answer is C) 10 multiple choice and 16 fill in the blank questions.