Percentages: Question 2

Worked solution

Part (a): reverse a percentage decrease

A reduction of $15\%$ means the sale price is what remains after $15\%$ is taken off, so the sale price represents

$100\% - 15\% = 85\%$

of the original price. Writing this as a decimal multiplier, the original price was multiplied by $0.85$ to give $612:

$\text{original} \times 0.85 = 612$

To reverse the change, divide by the multiplier (do not just take $15\%$ of $612):

$\text{original} = \frac{612}{0.85} = 720$

The original price of the tablet was $720.

Check: $720 \times 0.85 = 612$ ✓

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Part (b): reverse a percentage increase

An increase of $18\%$ means the new price represents

$100\% + 18\% = 118\%$

of the original price, i.e. a multiplier of $1.18$:

$\text{original} \times 1.18 = 1121$

Divide by the multiplier to undo the increase:

$\text{original} = \frac{1121}{1.18} = 950$

The price before the increase was $950.

Check: $950 \times 1.18 = 1121$ ✓

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Part (c): reverse two consecutive changes

Apply the two changes as multipliers, in order.

• An increase of $25\%$ is a multiplier of $1.25$.
• A reduction of $12\%$ is a multiplier of $0.88$ (since $100\% - 12\% = 88\%$).

Starting from the original price $P$:

$P \times 1.25 \times 0.88 = 1419$

Combine the two multipliers into a single overall multiplier:

$1.25 \times 0.88 = 1.1$

So

$P \times 1.1 = 1419 \quad\Longrightarrow\quad P = \frac{1419}{1.1} = 1290$

The original price of the laptop was $1,290.

Note: you cannot simply combine the changes as $25\% - 12\% = 13\%$. The correct combined multiplier is $1.25 \times 0.88 = 1.1$, an overall increase of $10\%$, not $13\%$.

Check: $1290 \times 1.25 = 1612.50$, then $1612.50 \times 0.88 = 1419$ ✓

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Final answers

• (a) $\boxed{720}$ dollars
• (b) $\boxed{950}$ dollars
• (c) $\boxed{1290}$ dollars