Discount and tax

A discount is a percentage decrease. When a 15% discount is applied, the customer pays the remaining percentage of the marked price.

The customer pays $100\%-15\%=85\%$ of the marked price.

$\text{Multiplier}=\frac{85}{100}=0.85$

The multiplier is 0.85. To verify: 0.85 \times \320 = $272$,whichislessthan$320, as expected for a discount.

We need the multiplier for a 15% discount — this should give a number less than 1, since the price decreases.

0.15 is the decimal form of 15% itself — it represents only the discount amount as a fraction of the price, not the selling price fraction. This is incorrect.

1.15 is used when adding 15% (like a tax), not subtracting it. This would give a price higher than the original, which is wrong for a discount.

0.75 corresponds to a 25% discount ($100\%-25\%=75\%$), not a 15% discount.

0.85 is correct because $100\%-15\%=85\%=0.85$. Multiplying by 0.85 gives the price after a 15% discount.

A 20% discount means the customer pays $100\%-20\%=80\%$ of the marked price. The multiplier is 0.80.

$\text{Selling Price}=0.80\times \$115.80$

$0.80\times \$115.80=\$92.64$

The selling price is **$92.64\ast \ast ,whichislessthan$115.80 — this makes sense for a discount.

We need the final price after a 20% discount on $\mathrm{115.80.}Theanswermustbe\ast \ast lessthan\ast \ast$115.80.

**$138.96\ast \ast isgreaterthanthemarkedpriceof$115.80. A discount always reduces the price, so this is impossible.

**$23.16\ast \ast isthediscountamountitself($0.20 \times $115.80 = $23.16$), not the selling price. The question asks for the selling price, not the discount.

**$95.80\ast \ast wouldresultfromsubtractingthepercentagenumberdirectly($$115.80 - 20 = $95.80$), which is a common mistake. The 20% must be calculated on the marked price first.

**$92.64\ast \ast iscorrect:$$115.80 - $23.16 = $92.64$,orequivalently$0.80 \times $115.80 = $92.64$.