Finding Price Changes in One Step

When you’re shopping at a store during a sale, it can be a bit tricky to calculate the new price by using the two-step method. Instead, you can use a simpler method: Rather than looking at the discount of $20$ %, you can imagine that you need to pay $80$ % of the old price.

Rule

You can find the new price by looking at what percentage of the old price you need to pay, rather than what percentage you need to subtract from the old price.

Keep in mind that the old price is $100$ %.

If $a % + b % = 100 %$ and you have an $a %$ discount, you have to pay $b %$ of the old price. This means that:

\begin{array}{l} new price & = b % \times old price \\ = \frac{b}{100} \times old price \end{array}

By finding the percentage of the old price you have to pay, you can find the new price in just one step.

Example 1

Here are a few examples:

$10$ % and $90$ % is a whole, because $10 % + 90 % = 100 % = 1$ .
$25$ % and $75$ % is a whole, because $25 % + 75 % = 100 % = 1$ .
Reminder: A $25$ % discount means that you pay $75$ % of the old price.

Example 2

A shirt used to cost $ $30$ , but is now on sale at a $20$ % discount. That means you need to pay $80$ % of the old price, which is $80$ % of $ $30$ . That gives you the following to work with:

\begin{array}{l} new price & = 80 % \times $ 30 \\ = \frac{80}{100} \times $ 30 \\ = 0.8 \times $ 30 \\ = $ 24 \end{array}

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Price Change and New Price in Two Steps

Estimates