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in Linear Equations by (30.8k points)
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Divide 150 into three parts such that the second number is five - sixths the first and the third number is four - fifths the second.

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Best answer

Let the first part be x of 150

According to the question second part is \(\frac{5}{6}\text{x}\)

And the third part is \(\frac{4}{5}(\frac{5}{6}\text{x})\)

Adding all of them

\(\text{x}+\frac{5}{6}\text{x}+\frac{20}{30}\text{x}=150\)

Taking LCM of 6 and 30 = 30

\(\Rightarrow \frac{30\text{x+25x+20x}}{30}=150\)

⇒ 75x = 150 × 30

\(\Rightarrow \text{x}=\frac{4500}{75}=60\)

Second part = \(\frac{5}{6}\text{x}=50\)

Third part = \(\frac{4}{5}(\frac{5}{6}\text{x})=40\)

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