Write final amount as original amount times the complete multiplier. Divide by that multiplier to reverse the change. Subtracting the same percentage from the final value uses the wrong base. Example After a 15% discount, a bag costs $68. Let its marked price be P dollars. 0.85P=68 P= 680.85 =80 The marked price was $80; checking, 15% of $80 is $12. For several changes, divide by the product of all multipliers. A 100% decrease has multiplier 0. Its result cannot determine the original amount, so reverse division is impossible.

Write final amount as original amount times the complete multiplier. Divide by that multiplier to reverse the change. Subtracting the same percentage from the final value uses the wrong base.

After a $15\%$ discount, a bag costs $\$68$. Let its marked price be $P$ dollars.

$\begin{aligned}0.85P&=68\\P&=\dfrac{68}{0.85}\\&=80\end{aligned}$

The marked price was $\$80$; checking, $15\%$ of $\$80$ is $\$12$. For several changes, divide by the product of all multipliers.

A $100\%$ decrease has multiplier $0$. Its result cannot determine the original amount, so reverse division is impossible.

Recovering an original amount

Recovering an original amount