A test has twenty questions worth 100 points. The test consists of True/ False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?
T/F ---- x
multiple choice --- y
x+y = 20 ----> y = 20-x
3x + 11y = 100
3x + 11(20-x) = 100
3x + 220 - 11x = 100
-8x = -120
x = 15 and then y = 5
There are 5 multiple choice questions
Let's assume the number of multiple choice questions on the test is x.
The number of True/False questions is given by 20 - x, since there are a total of twenty questions on the test.
The score from the True/False questions is calculated as (20 - x) * 3.
The score from the multiple choice questions is calculated as x * 11.
The total score for the test is 100.
So, we can formulate the equation:
(20 - x) * 3 + x * 11 = 100
Now, let's solve this equation to find the value of x.
To find the number of multiple choice questions on the test, we can use the information given.
Let's assume the number of multiple choice questions is "x".
Each multiple choice question is worth 11 points, so the total score for all multiple choice questions would be 11x.
The test has twenty questions in total, including both true/false and multiple choice questions.
So, the total number of true/false questions would be 20 - x.
Each true/false question is worth 3 points, so the total score for all true/false questions would be 3 * (20 - x).
The total score for the test is 100 points, so we can create the equation:
11x + 3 * (20 - x) = 100
Now, we can solve this equation for x to find the number of multiple-choice questions.
11x + 60 - 3x = 100
8x + 60 = 100
8x = 100 - 60
8x = 40
x = 40/8
x = 5
Therefore, there are 5 multiple-choice questions on the test.