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    Topics || Problems

    A line 20 inches long is divided into two parts whose lengths have the ratio 3:7. Find the lengths of the parts.

    Solution:

    Let \(x\) be the first part and \(y\) be the second part.

    \(x + y = 20\)

    The ratio is 3:7, thus \(3:7 = x:y\)

    \(\frac{3}{7} = \frac{x}{y}\)

    \(x = \frac{3y}{7}\)

    \(\frac{3y}{7} + y = 20\)

    \(\frac{10y}{7}=20\)

    \(y = 14\)

    \(x = 20-14 = 6\)

    Thus, the length of the shorter part is 6 inches and the longer part is 14 inches.