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Mathematics

Solve the following equation and check your answer:

x - 24% of x = 38

Linear Eqns One Variable

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Answer

We have:

=x−24% of x=38⇒x−24100x=38⇒100x−24x100=38⇒76x100=38⇒76x=38×100⇒76x=3800⇒x=380076\phantom{=} x - 24\% \text{ of } x = 38 \\[1em] \Rightarrow x - \dfrac{24}{100}x = 38 \\[1em] \Rightarrow \dfrac{100x - 24x}{100} = 38 \\[1em] \Rightarrow \dfrac{76x}{100} = 38 \\[1em] \Rightarrow 76x = 38 \times 100 \\[1em] \Rightarrow 76x = 3800 \\[1em] \Rightarrow x = \dfrac{3800}{76}

∴ x = 50

Check:

LHS = x - 24% of x

= 50 - 24% of 50

= 50 - 12

= 38

RHS = 38

Hence, LHS = RHS.

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