Math CentralQuandaries & Queries


Question from Kenneth:


1. If 63 books cost $126, what will 125 books cost?

Calculation: ($126 X 125)/63

Explanation: If 63 books cost $126, each book will cost one sixty-third of $126, which is expressed by 63 below the divisor line.
125 books will cost 125 times this number of dollars, which is expressed by writing 125 above the line as a factor of the dividend.
The result is $250.


If 15 men can do a piece of work in 7 days, in how many days can 21 men do the same work?

2. I think the calculation is (15 men X 7 days)/21 men


Can you use a similar explanation from the first example to explain how the
answer is determined for the second example?

Which would be used 15 men/21 men X 7 days or 7 days/21 men X 15 men or something else and why?

I thank you for your reply.

Hi Kenneth,

Your solution to the first problem is fine.

For the second problem when you tell me "15 men can do a piece of work in 7 days" I wonder how big the job is. One measure is that it is 15 × 7 man days (the units are man × days). If you have 21 men to work on this job it will take (15 × 7 man days)/(21 men) = 5 days.

This calculation of the size of the job is exactly what you would do if you were a contractor. You are going to hire some men for this job and you need to know how much it will cost you. It will cost you 15 × 7 man days and if you know how much you pay per day you can get an answer in dollars. If you have 21 men to work on the job you cakenneth

n complete it sooner but it still costs you 15 × 7 man days.

I hope this helps,

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