There are 35 problems that are worth 2 or 6 points. there are 110 points available on the test. find the number of each type of test question.

There are 25 two point questions, and 10 six point questions

Step-by-step explanation:

First note that if all the questions were value 6, this would give 6x35 = 210 points.

Each time we swap a 6 point question to a 2 point question, the totl points decrease by 4.

So as 110 is 100 less then 210, and 100÷4 =25, this means we know that if we decrease the number of 6 point questions from 35 to 10 (i.e. 35-25), this should give the answer.

So i.e. there are 10 six point questions, meaning there are 35-10 = 25 two point questions. (we can also check this does indeed give 110, as

10x6 + 25 x2 = 60 +50 = 110 )