Your teacher is giving you a test worth 100 points containing 40 questions there are 2-point and 3 point questions on the test how many each type are on the test ?

You can set up a system of equations:

let x=number of 2-point questions, then
40-x = number of 3-point questions.

2(x) + 3(40-x) = 100
Solve for x.

Or you can solve mentally as follows:
If all questions are worth 2-point, then the total = 2*40=80 points, or 20 points too few.
Exchange 20 of the questions for 3 points will therefore give a total of 100 points, leaving 20 2-pointers, and 20 3-pointers.

To find out how many 2-point and 3-point questions are on the test, we can set up two equations.

Let's assume the number of 2-point questions is 'x' and the number of 3-point questions is 'y'.

The total number of questions is given as 40, so we have the equation:

x + y = 40 ---(1)

The total number of points for the test is given as 100. Since each 2-point question contributes 2 points and each 3-point question contributes 3 points, we have the equation:

2x + 3y = 100 ---(2)

Now, we can solve these two equations simultaneously to find the values of 'x' and 'y'.

One way to solve these equations is by substitution.

From equation (1), we can express 'x' in terms of 'y':

x = 40 - y

Substituting this expression for 'x' in equation (2), we get:

2(40 - y) + 3y = 100

Simplifying the equation:

80 - 2y + 3y = 100

Combining like terms:

80 + y = 100

Subtracting 80 from both sides:

y = 100 - 80

y = 20

Now, substitute the value of 'y' back into equation (1) to find 'x':

x + 20 = 40

x = 40 - 20

x = 20

So, there are 20 two-point questions and 20 three-point questions on the test.