Question 1069703
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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

{{{(1/2)x}}} = {{{(1/3)y}}},       (2)

{{{(1/3)y}}} = {{{(1/4)z}}}        (3)


From (2),  y = {{{(3/2)x}}},  z = {{{(4/3)y}}} = {{{(4/3)*(3/2)x}}} = 2x. 

Substitute it into (3), and you will get


{{{x + (3/2)x + 2x}}} = 243,   or

4.5x = 243.


x = {{{243/4.5}}} = 54.


Then  y = {{{(3/2)*54}}} = 81  and  z = 2x = 108.
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