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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: new price = b% ×old price = b 100 ×old price

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: new price = 80% ×$30 = 80 100 ×$30 = 0.8 ×$30 = $24

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