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?

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.

**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%

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%$30−20%

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 maths speak for "use multiplication."

There are two ways of calculating discounts to find the sales price of item. We will look at both way using the tablet example above. You can use either method and they should both give you the same answer.

Store A was charging $\$350$$350 with a $20%$20% discount. So to calculate the discount, we need to find $20%$20% of $\$350$$350:

$\$350\times20%=\$70$$350×20%=$70

Then we can take the discount amount of $\$70$$70 away from the regular price to give us the sale price at store A:

$\$350-\$70=\$280$$350−$70=$280

So you could buy the tablet at store A for $\$280$$280.

This way seems a bit theoretical at first but can make for quick calculations once you get the hang of it. The **regular price** represents the **whole** or $100%$100% of the price. A 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=90$100−10=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 B, which was offering the tablet for $\$335$$335 with a $15%$15% discount.

So firstly, how much of the regular price would remain after a $15%$15% discount?

$100-15=85%$100−15=85%

So now we can calculate $85%$85% of the regular price to give us the sale price.

$\$335\times85%=\$284.75$$335×85%=$284.75

So even though store B had a cheaper regular price, store A offered a slightly better sales price. Switch calculation methods between the stores and you will see that you get the same answer regardless of what method you use.

We may also want to calculate which item is better value. To do this, we need to find a common amount to compare. Often it's easiest to find the *unit price* of each item, where we find the cost per unit of measurement, for example per litre, per kilogram or per item. We can also compare the *amount per dollar,* where we work out how much of something we would get for $\$1$$1.

For example, are you better off paying $\$10.50$$10.50 for $3$3kg of apples or $\$6.20$$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$$10.50 for $3$3kg | $\$6.20$$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 $2$2kg of apples because it's a cheaper price per kilogram.

If Bill's Brand sells $200$200 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 | $=$= | $8.33$8.33... grams |

So at Bill's, we'd get approximately $8.33$8.33 grams of cement for a dollar.

Bob's:

$\$13$$13 | $=$= | $150$150 grams | (divide both sides by $13$13) |

$\$1$$1 | $=$= | $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.

A TV normally sells for $£2300$£2300.

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

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

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.

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

Give your answer correct to the nearest penny.

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