SOLUTION: Divide n into 3 parts such that the first shall be one-rth of the second and one-kth of the third.

Question 344976: Divide n into 3 parts such that the first shall be one-rth of the second and one-kth of the third.
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
Divide n into 3 parts such that the first shall be one-rth of the second and one-kth of the third.

Let x be the first part of n
Let y be the second part of n
Ley z be the thitrd part of n

Then 

x + y + z = n

>>...the first shall be one-rth of the second...<<

x = *y

>>...the first shall be...one-kth of the third...<<

x = *z

So we have this system of three equations and three unknowns:



Clearing the 2nd and 3rd of fractions:



Substituting rx for y and kx for z in the first equation:







Since ,





Since ,





So the parts are

, , 

Edwin

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