 Lesson Everyone loves a great deal or a 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 device. 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 shops advertising, "$25%$25% off," "pay less when you pay cash" and so on. These are all examples of shops offering discounts. A discount is basically a reduction in price, whether it be on goods or services. Businesses often use discount sales as a way of enticing people 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 (i.e. The non-sale price).

Sale price: The price after a discount is given.

Percentage discount: The amount of discount received expressed 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%

### Amount per unit

For example, are you better off paying $\$10.50$$10.50 for 33kg of apples or \6.20$$6.20 for $2$2kg of apples? An easy way to compare the two options is to find the price per kilogram for each option.

 $\$10.50$$10.50 for 33kg \6.20$$6.20 for $2$2kg Divide by $3$3 to get the price per kilo Divide by $2$2 to get the price per kilo $\$3.50$$3.50/kg \3.10$$3.10/kg

So you're better off paying $\$6.20$$6.20 for 22kg of apples because it's a cheaper price per kilogram. ### Amount per dollar If Bill's Brand sells 200200 grams of cement for \24$$24 and Bob's Brand sells $150$150 grams of the same cement for $\$13$$13, which is better value? Let's see how much cement we would get for one dollar at each shop: Bill's:  \24$$24 $=$= $200$200 grams (divide both sides by $24$24) $\$1$$1 == 8.338.33... grams So at Bill's, we'd get approximately 8.338.33 grams of cement for a dollar. Bob's:  \13$$13 $=$= $150$150 grams (divide both sides by $13$13) $\$11 $=$= $11.53$11.53... grams

We get approximately $11.5$11.5 grams of cement at Bob's, which is much better value than at Bill's.

#### More Worked Examples

##### Question 1

A TV normally sells for $£2300$£2300.

1. If the TV has a discount of $£340$£340, calculate the discount as a percentage of the normal price.

2. If the TV is on sale for $£1970$£1970, calculate the discount as a percentage of the normal price.

##### QUESTION 2

A direct factory outlet sells $40$40 L of detergent for $£694$£694 to the public. Meanwhile, the local hardware store sells $8$8 L of the same detergent for $£92$£92.

1. Calculate the discount in pounds per litre when buying from the hardware store rather than the direct factory outlet.

There is a $11%$11% off sale in store. Calculate the regular price, to the nearest penny, of an item that sells for £190.