Question 208016: In a 3 hour examination of 350 questions, there are 50 math problems. If twice as much time should be allowed for each math problem as for each of the other questions, how many minutes should be spent on the math problems.
I used 300x+(50*2x)=180 giving me x=.45
The decimal in the answer is throwing me off. Is there a better way of solving?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! In a 3 hour examination of 350 questions, there are 50 math problems. If twice as much time should be allowed for each math problem as for each of the other questions, how many minutes should be spent on the math problems.
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3 hour exam with 350 questions.
50 math problems
300 other problems.
let x = amount of time for the other problems.
let 2x = amount of time for the math problems.
total time is 3 hours.
3 hours = 50 * (2x) + 300 * (x)
this becomes 100 * x + 300 * x = 3
change to minutes this becomes 100 * x = 300 * x = 180
combine like terms to get 400 * x = 180
divide both sides by 400 to get x = 180 / 400 = .45 minutes
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.45 minutes should be allowed per other problem.
2 * .45 = .90 minutes should be allowed per math problem.
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50 * .90 + 300 * .45 = 180.
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the decimal is correct.
.45 * 60 seconds per minute = 27 seconds per other problem.
.9 * 60 seconds per minute = 54 seconds per math problem.
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50 * 54 = 2700 seconds for all math problems.
300 * 27 = 8100 seconds for all other problems.
2700 + 8100 = 10,800 seconds overall
divide by 60 to get 180 minutes
divide by 60 to get 3 hours
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your answer was good.
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