Question 29673: Your teacher is giving you a test worth 100 points containing 40 questions. There are two point and four point questions on the test. How many of each type of question are on the test?
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! Your teacher is giving you a test worth 100 points containing 40 questions. There are two point and four point questions on the test. How many of each type of question are on the test?
Let the number of 2-point questions be T
and let the number of 4-point questions be F
Total number of questions = 40
Therefore T + F = 40 ----(1)
Total number of points = 100
That means total points out of 2-point questions
together with the total points out of 4-point questions is 100
That 2T + 4F = 100 ----(2)
[one 2-point question = 2-points
and therefore T, 2-point questios = 2XT = 2T points
one 4-point question = 4-points
and therefore F, 4-point questios = 4XF = 4F points]
(1) implies T = (40-F) ----(*)
Putting (*) in (2)
2T+4F = 100
2(40-F)+4F = 100
80-2F+4F = 100
(-2F+4F)= 100-80 (grouping like terms,changing sign while changing side)
2F = 20
F = 20/2 = 10
Therefore the number of 4-point questions = 10
Putting F= 10 in (*),
T = 40-F = 40-10 = 30
Therefore the number of 2-point questions =30
Verification:30 questions each of 2-points give 30X2 = 60
10 questions each of 4-points give 10X4 = 40
These points add up to 100.
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