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Word Problems/Compound Proportions

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Question
Hello:

Four carpenters can build eight houses in ten days. Two carpenters  can build how may houses in 15 days?

I used this solution:

8 houses = (constant) X 4 carpenters X 10 days

The constant represents the 8/(4 X 10) or 8/40 or 1/5

So, 8 = (1/5) X 4 X 10. Now the missing number can be determined by using a similar calculation:

unknown houses = 1/5 X 2 carpenters X 15 days

unknown houses = 1/5 X 30 = 6 or 6 houses

However this solution does not work if one of the other amounts is unknown.  For example, we know that four carpenters can build eight houses in ten days. But how many days can two carpenters build six houses?

This solution is incorrect:

10 days = (constant) X 4 carpenters X 8 houses

10/(4 X 8) = 10/32

? days = (10/32) X 2 carpenters X 6 houses does not give the correct answer. The correct answer is 15 days

Do you know the correct constant to use in the solution?

I thank you for your reply.

Answer
"Four carpenters can build eight houses in ten days."
8 houses per 40 carpenter-days = ⅕ house per carpenter-day

"Two carpenters can build how may houses in 15 days?"
2 carpenters 15 days = 30 carpenter-days
30 carpenter-days ⅕ house per carpenter-day = 6 houses

"in how many days can two carpenters build six houses?"
6 houses (1 carpenter-day)/(⅕ house) = 30 carpenter-days
30 carpenter-days (2 carpenters) = 15 days

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Janet Yang

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Word problems are my favorite type of math questions! I would not feel comfortable answering questions that require specialized knowledge (Physics, Statistics, etc.) because I have not studied these in depth.

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I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

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I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley, and a Master of Business Administration degree from The Wharton School.

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