Ms. Townsend is giving a test worth 100 points with 40 questions. There are two-point questions and four-point questions. How many of each type of question are on the test?
If there are x worth 2 points, then the rest (40-x) are worth 4 points.
2x + 4(40-x) = 100
Now finish it off
Let's assume there are x two-point questions and y four-point questions on the test.
The total number of questions is given as 40, so we have the equation:
x + y = 40 ----(1)
The total value of the test is given as 100 points, so we have the equation:
2x + 4y = 100 ----(2)
To solve the system of equations (1) and (2), we can use substitution or elimination method.
Let's solve using the elimination method. Multiply equation (1) by 2 to make the coefficients of x match:
2(x + y) = 2(40)
2x + 2y = 80 ----(3)
Now we can subtract equation (3) from equation (2) to eliminate the x variable:
(2x + 4y) - (2x + 2y) = 100 - 80
2y = 20
Divide both sides by 2:
2y/2 = 20/2
y = 10
Now substitute the value of y back into equation (1):
x + 10 = 40
x = 40 - 10
x = 30
Therefore, there are 30 two-point questions and 10 four-point questions on the test.
To solve this problem, you need to set up a system of equations based on the given information.
Let's assume the number of two-point questions is x and the number of four-point questions is y.
According to the problem, there are 40 questions in total, so we can write the equation:
x + y = 40. (equation 1)
Additionally, each two-point question is worth 2 points, and each four-point question is worth 4 points. Since the test is worth 100 points in total, we can write the second equation:
2x + 4y = 100. (equation 2)
We now have a system of two equations (equation 1 and equation 2) with two variables (x and y). We can solve this system to find the values of x and y.
First, let's start by solving equation 1 for x:
x = 40 - y.
Now, substitute this value of x into equation 2:
2(40 - y) + 4y = 100.
Simplifying the equation:
80 - 2y + 4y = 100,
2y = 100 - 80,
2y = 20,
y = 20/2,
y = 10.
Therefore, there are 10 four-point questions on the test.
Now, substitute the value of y back into equation 1 to find x:
x + 10 = 40,
x = 40 - 10,
x = 30.
Hence, there are 30 two-point questions on the test.