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If \(3\%\) of \((a + b) = 7\%\) of \((ab)\) and \(5\%\) of \((a - b) = 4\%\) of \((ab)\), then what…

From the two conditions, \(\frac{3}{100}(a+b) = \frac{7}{100}(ab)\) and \(\frac{5}{100}(a-b) = \frac{4}{100}(ab)\), so \(\frac{3(a+b)}{7} = \frac{5(a-b)}{4}\). Cross…

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If 3%3\% of (a+b)=7%(a + b) = 7\% of (ab)(ab) and 5%5\% of (a−b)=4%(a - b) = 4\% of (ab)(ab), then what percentage of bb is aa?

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From the two conditions, 3100(a+b)=7100(ab)\frac{3}{100}(a+b) = \frac{7}{100}(ab) and 5100(a−b)=4100(ab)\frac{5}{100}(a-b) = \frac{4}{100}(ab), so 3(a+b)7=5(a−b)4\frac{3(a+b)}{7} = \frac{5(a-b)}{4}. Cross multiplying gives 12(a+b)=35(a−b)12(a+b) = 35(a-b), hence 47b=23a47b = 23a and ab=4723\frac{a}{b} = \frac{47}{23}. Expressed as a percentage, aa is 470023%\frac{4700}{23}\% of bb.

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