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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
= .
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.