Question 1005787: Please help me solve this weighted average problem ;
Your friends math test contained 42 questions some of which were worth 2 points , while the rest were worth 3 points.Your friend tells you that a perfect score is 100 points, but she cannot remember how many of each type were on the test . Help your friend out , how many of each type were on the test?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
x = number of 2 point questions
y = number of 3 point questions
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There are 42 questions total, so,
x+y = 42
solve for y to get
y = 42-x
y = -x+42
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There are x questions that are 2 points each. In total, we have 2x points just for these types of questions.
There are y questions that are 3 points each. In total, we have 3y points just for these types of questions.
The grand total is 2x+3y points. We're given the grand total to be 100.
So the second equation is 2x+3y = 100
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Now we will replace the y in the second equation with -x+42 then solve for x
2x+3y = 100
2x+3(-x+42) = 100
2x-3x+126 = 100
-x+126 = 100
-x+126-126 = 100-126
-x = -26
x = 26
Use this x value to find the value of y
y = -x+42
y = -26+42
y = 16
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Summary:
x = 26 and y = 16
There are 26 two point questions and 16 three point questions.
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