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Word Problems/Compound Proportions

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Question
The following is an example as to how to solve a compound proportion.  

Quantity 1----Quantity 2----Quantity 3
----a-------------b-------------c
----d-------------e-------------?
 

If quantity 1 and quantity 2 are [directly related] and quantity 2 and quantity 3 are also [directly related], then use the following rule:

(a X b)/c = (d X e)/?

Example:
If 195 men working 10 hours a day can finish a job in 20 days. How many men employed are needed to finish the job in 15 days if they work 13 hours a day?

Solution:


Days----Hours-------Men
20--------10--------195
15--------13--------?

20 X 10 X 195 = 15 X 13 X ?

(20 X 10 X 195)/(15 X 13) = ?

I can see by what is shown above that the days decrease and the hours increase. Is this "directly related" and/or "indirectly related" information? So using this information, how can it solve this by using the calculation (20 X 10 X 195)/(15 X 13) = ?

I thank you for your reply.

Answer
Yes, that's the correct way to do it.
By the way, the 15 is 5x3, so 20/5 =4 and 195/3 = 65.
This is then 4 x 10 x 65 / 15.
Now 10/15 = 2/3, so we have 4 x 2 x 65 / 3 = 8 x 65 / 3 = 520/3 = 173 1/3.

This is the number of men, which is suppose to be an integer,
so round up to 174 to make sure it gets done on time.

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