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Mathematics

If x varies directly as y and x = 150 when y = 50. Find:

  1. x, when y = 12.5

  2. y, when x = 75

Direct & Inverse Variations

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Answer

  1. Since it is a case of direct variation,

15050=x12.5⇒31=x12.5⇒x=3×12.5⇒x=37.5\dfrac{150}{50} = \dfrac{x}{12.5}\\[1em] \Rightarrow \dfrac{3}{1} = \dfrac{x}{12.5}\\[1em] \Rightarrow x = 3 \times 12.5\\[1em] \Rightarrow x = 37.5

Hence, when y = 12.5, then x = 37.5.

  1. Since it is a case of direct variation,

15050=75y⇒31=75y⇒y=753⇒x=25\dfrac{150}{50} = \dfrac{75}{y}\\[1em] \Rightarrow \dfrac{3}{1} = \dfrac{75}{y}\\[1em] \Rightarrow y = \dfrac{75}{3}\\[1em] \Rightarrow x = 25

Hence, when x = 75, then y = 25.

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