A test has 15 questions worth 100 points in total. The test consists of multiple choice questions, which are 4 points each, and open-response questions, which are worth 12 points each. How many multiple choice questions are on the test?
Let X= multichoiceques,and Y=openQUES,(simulta,eqn) 4X+12Y=100,X+Y=15,then get your ans
Let's assume the number of multiple choice questions is "x" and the number of open-response questions is "y".
According to the given information, the total number of questions on the test is 15:
x + y = 15 Equation 1
The value of each multiple choice question is 4 points, so the total points from the multiple choice questions is 4x.
The value of each open-response question is 12 points, so the total points from the open-response questions is 12y.
The total points from all the questions is 100:
4x + 12y = 100 Equation 2
To solve these equations, we can use either substitution or elimination method.
Using substitution:
From Equation 1, we can express x in terms of y:
x = 15 - y
Substituting this value of x in Equation 2:
4(15 - y) + 12y = 100
60 - 4y + 12y = 100
8y = 100 - 60
8y = 40
y = 40/8
y = 5
Substituting this value of y in Equation 1:
x + 5 = 15
x = 15 - 5
x = 10
Therefore, there are 10 multiple choice questions on the test.
To determine the number of multiple-choice questions on the test, we need to know the total number of points for the multiple-choice questions and the number of points each multiple-choice question is worth.
Since each multiple-choice question is worth 4 points, we can calculate the total number of points for the multiple-choice questions by multiplying the number of multiple-choice questions by 4.
Let's say the number of multiple-choice questions is 'x.' The total point value of the multiple-choice questions is 4 * x.
We are given that the total point value of the test is 100 points, so we can set up the equation:
4 * x + 12 * (15 - x) = 100
We subtract 'x' from 15 because the remaining questions are open-response questions.
Simplifying the equation, we have:
4x + 180 - 12x = 100
Combine like terms:
-8x = -80
Divide both sides by -8:
x = 10
Therefore, there are 10 multiple-choice questions on the test.
If there are x multiple-choice questions, then there are 15-x open ones.
4x + 12(15-x) = 100