Exercise 39

A retailer increases the price of its merchandise by 20% before promoting a 20% discount. The new selling price, relative to the original (\(x\)), is:

  1. \( x \)

  2. \( \cfrac{x}{20} \)

  3. \( \cfrac{24x}{25} \)

  4. \( \cfrac{19x}{25} \)

  5. \( \cfrac{14x}{25} \)

Try to solve it before checking the answer.

  1. \( \cfrac{24x}{25} \)

If the original price is \( x \), the 20% increase is \( 0.2x \). Then, the increased price is:

\[ x + 0.2x = 1.2 x \]

The 20% of this increased price is:

\[ 0.2 (1.2 x) = 0.24 x \]

Therefore, the new price, after the 20% discount, is:

\[ \begin{aligned} 1.2x – 0.24x &= 0.96x \\[.5em] &= \frac{96}{100} x \\[.5em] &= \frac{24}{25} x \\[.5em] &= \boldsymbol{ \frac{24x}{25} } \end{aligned} \]

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