 4.05 Discounts and markups

Lesson Everyone loves a great deal or sale when they're shopping! However, most products today come in different varieties and are sold at more than one store. For example, say you were going to buy a new tablet. Store A is charging $\$350$$350, with a 20%20% discount and Store B is charging \335$$335 with a $15%$15% discount. How do you work out which store will give you the best price?

Discounts

Let's start by talking about discounts. Everyone will have seen stores advertising, "$25%$25% off", "pay less when you pay cash" and so on. These are all examples of discounts. A discount is basically a reduction in price (often a percent decrease), whether it be on goods or services. Businesses often use discount sales to encourage people to buy from them so it's important to be able to calculate discounts to make sure you're getting a great deal.

Definitions

Regular price: The price before any discount is given (the non-sale price).

Sale price: The price after a discount is given.

Percentage discount: The amount of discount received expressed as a percentage (usually of the regular price but this may change depending on the question).

To work out the percentage discount, we use the formula:

$\text{Percentage discount}=\frac{\text{discount }}{\text{regular price}}\times100%$Percentage discount=discount regular price×100%

A common mistake

When working with percentages, students often subtract the percentage from the regular price. For example, if a t-shirt cost $\$30$$30 and had 20%20% off, some students may write: 30-20%3020% But this doesn't specify what they're finding 20%20% of and as such, can cause problems doing calculations. Remember we need to find 20%20% of the original price, which is math speak for "use multiplication." Calculating discounts to find sales prices There are two methods for calculating discounts to find the sales price of item. We will look at both ways using the example of the tablet from above. You can use either method and they will both give you the same answer. Recall that store A was charging \350$$350 with a $20%$20% discount.

Method 1: Calculate the sales price and subtract it from the regular price
Find $20%$20% of $\$350$$350 350\times20%=\70350×20%=70 Now we know the sale is for \70$$70 off
Subtract $\$70$$70 from the original price of \350$$350 $350-70=\$280$35070=$280
So the sale price of the tablet at store A is: $\$280$$280 The next method can make for quick calculations once you get the hang of it. For this method you need to think of the regular price as the whole or 100%100% of the price. The sale price can be expressed as the remaining percentage after a discount has been taken away. So if an item had a 10%10% discount, 100-10=9010010=90, so the sale price would be 90%90% of the original price. Let's use this method to calculate the sale price at store A and compare it with our result from Method 1. Method 2: Calculate the sales price as a percentage of the regular price With a 20%20% discount what percentage remains? 100-20=80%10020=80% Calculate 80%80% of the regular price. 350\times80%=\280350×80%=280 Again we find the sale price of the tablet at store A is: \280$$280

Now calculate the sale price of the tablet at store B using the method you prefer. Recall store B was offering the tablet for $\$335$$335 with a 15%15% discount. Did you find that the sale price of the tablet at store B to be \284.75$$284.75? So even though store B had a cheaper regular price, store A offered a slightly better sales price resulting in a better deal overall.

Worked examples

Question 1

At the end of the year, a television, originally advertised at $\$3800$$3800. Valentina pays \3610$$3610for the television. What percentage discount did she receive?

First, calculate what percentage the sale price is of the regular price.

Think: How do we calculate a percentage?

Do:

Outcomes

8.4

Solve practical problems involving consumer applications