SOLUTION: devide 240 in two parts in the ratio 5:7.

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Question 1148677: devide 240 in two parts in the ratio 5:7.
Answer by ikleyn(52778) About Me  (Show Source):
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highlight%28cross%28devide%29%29 divide 240 in two parts in the ratio 5:7.
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Let x be the shorter part; then the longer part is (240-x).


And the condition says that


    x%2F%28240-x%29 = 5%2F7.


Cross-multiply


    7x = 5*(240-x)

    7x = 1200 - 5x

    7x + 5x = 1200

    12x     = 1200

      x     = 1200/12 = 100.


ANSWER.  The parts are  100  and  140.

Solved.

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The shorter solution is possible, too (for more advanced students). 

From the condition, the parts are 5x and 7x, where "x" is the common measure of the parts.


Then 5x + 7x = 240,  12x = 240  and  x= 20.


It implies that the parts are  100 and 140, exactly as in the previous solution.


You can choose EITHER solution depending on your level and preferences.