A math test is worth 100 points as has 38 problems each problem is worth either five. Or two. How many problems of each. Values are on the test

Question

there are      two-point problems.

there are      five-point problems.

Answer 1

Let P2 is the problem that is worth 2 points   and  P5 the problem that is worth 5 points

we will have:  P2 + P5 = 38 (1)   we will also have:  2P2 + 5P5 = 100 (2)

from the (1) we get P2 = 38 - P5  substituting on (2) where P2 = 38 - P5 we get  2(38 - P5) + 5P5 = 100

->> 76 - 2P5 + 5P5 = 100  ->>   3P5 = 100 - 76  ->>  3P5 = 24 ->> P5 = 24/3 = 8  so the 5 points problems

are 8  substituting to (1) where P5 = 8  we get  P2 = 38 - P5 ->> P2 = 38 - 8 = 30  So the 2 points problems

are 30

So we will have 8 * 5 = 40   and. 30 * 2 = 60  so total problems 40 + 60 = 100