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Estimates

You can use a simpler version of the one-step method to make quick estimates for the new price when you’re in a store that is having a sale, and it’s not important to get the new price exactly down to the penny. If the old price doesn’t end in a zero, you can round to the nearest ten or hundred first, depending on the scenario, and then use the method.

Rule

Estimating the New Price

If you know the the old price and the discount is $n %$ , then you have to pay $p % = 100 % - n %$ of the old price. You can estimate the new price like this:

Round the old price to the nearest 100 dollars. How many hundred dollar bills are there in the rounded price?
Multiply $p$ dollars by the number of hundred dollar bills, and you have your estimate.

Example 1

A PlayStation 5 used to cost $ $430$ , but is now discounted by $20$ %. You round the price down to $ $400$ . You have to pay $80$ % of the old price, which is $80 % \times $ 100 = $ 80$ for each hundred dollar bill in the estimate for the old price. As this is just an estimate, you don’t consider the extra $ $30$ for now.

That means the estimated price is

$ 80 \times 4 = $ 320

You continue with Example 1, and make the estimate a bit more accurate:

Example 2

The estimate is a bit more accurate if you add the $ $30$ you left behind earlier:

$ 80 \times 4 + $ 30 = $ 320 + $ 30 = $ 350

If you use a calculator to find the exact answer of $ $344$ , you will see that it’s a bit lower than your estimate. The reason why this happens is that the exact calculation also gives you a discount on the $ $30$ you left behind when you rounded.

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Finding Price Changes in One Step

Activities 3