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Number Theory/Algebra Solution



Can the answer to the following be determined by using algebra?  If so, what would be the solution?

4 carpenters can build 8 houses in 10 days.  2 carpenters can build how many houses in 15 days?

Answer: 6 houses

I thank you for your reply.

Hello Kenneth

I don't think we need algebra.  In the given information, 8 houses were built with 40 carpenter days of work.  So each house takes 5 carpenter days. In the problem we have 30 carpenter days, so 6 can be built.
However we can use the idea of joint proportionality.  The number of houses built is jointly proportioal to the number of carpenters and the number of days.  So h = kcd where k is a constant.  Substituting the given: 8 = k*40, so k = 1/5.  Our formula is then h = cd/5.
Best wishes

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