A history test is to have 20 questions in which some are multiple choice and some are essay. The multiple choice questions are worth 4 points each and the essay questions are worth 8 points each. if the test has a total of 100 points, how many of each type of question is on the exam?
m=number of multiple choice questons,
e=number of essay questions. = (20-m)
4*m + 8(20-m) = 100
Solve for m.
8m+160m=100
168m=100
m=100รท168
m=25/42.
25/42
To solve this problem, let's use the following variables:
- Let "x" represent the number of multiple-choice questions.
- Let "y" represent the number of essay questions.
Given that there are 20 questions in total, we can write the equation:
x + y = 20 (Equation 1)
We also know that multiple-choice questions are worth 4 points each, and essay questions are worth 8 points each. Therefore, the equation for the total points is:
4x + 8y = 100 (Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) that can be solved simultaneously to find the values of "x" and "y".
We can rewrite Equation 1 as:
x = 20 - y
Substituting this value of "x" into Equation 2, we get:
4(20 - y) + 8y = 100
Simplifying the equation:
80 - 4y + 8y = 100
4y = 100 - 80
4y = 20
y = 20/4
y = 5
Now, substituting the found value of "y" back into Equation 1, we can solve for "x":
x + 5 = 20
x = 20 - 5
x = 15
Therefore, there are 15 multiple-choice questions and 5 essay questions on this history test.