Question 182434: hi i'm having an extreme amount of trouble setting up word problems for linear equations , especially this one .
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 Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! hi i'm having an extreme amount of trouble setting up word problems for linear equations , especially this one .
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?
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Word problems are the scourge of the known universe. Maybe humans made a mistake by learning language. Anyway,
to save typing, use t for the two point questions and f for the four point questions.
t+f = 40 (there are 40 questions total)
2t+4f = 100 (2 points for each t, 4 for each f, 100 total)
Now, it's a math problem, 2 equations in 2 unknowns.
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t+f = 40 (no talking)
2t+4f = 100 --> t+2f = 50 (divided by 2)
t+f = 40 (still)
t+2f = 50
---------------- Subtract
0t-f = -10
f = 10 (10 4-point questions)
t = 30 (must be 30, there are 40 total)
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