SOLUTION: Divide 243 into 3 parts such that half of the first part,one-third of the second part and one-fourth of the third part are all equal.

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Question 1069703: Divide 243 into 3 parts such that half of the first part,one-third of the second part and one-fourth of the third part are all equal.
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!



Clear of fractions and solve the system.

Edwin

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
First part of the condition says 

x + y + z = 243,     (1)   

where x is the first quantity, y is the second and z is the third.


Second part of the condition gives these equalities

%281%2F2%29x = %281%2F3%29y,       (2)

%281%2F3%29y = %281%2F4%29z        (3)


From (2),  y = %283%2F2%29x,  z = %284%2F3%29y = %284%2F3%29%2A%283%2F2%29x = 2x. 

Substitute it into (3), and you will get


x+%2B+%283%2F2%29x+%2B+2x = 243,   or

4.5x = 243.


x = 243%2F4.5 = 54.


Then  y = %283%2F2%29%2A54 = 81  and  z = 2x = 108.