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 ?

Answer 1

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.