# Sales Discount Trickery

## From the Book

*Late Night Shopping Super Sale. Take 50% off the marked price, and then take a further 45% off that.*

“Bingo,” he said, a grin spreading over his face. He nodded towards the huge, gaudy banner still being hung by a shop assistant. “I told you.”

“It’s not going to work,” Eliza said, not looking up from her phone, her slim fingers flicking over the virtual keyboard. Light from the screen flashed on her black-rimmed, rectangular glasses. “No one’s dumb enough to fall for it.”

“Not even Carl?” Will said.

## The Problem

Will is attempting to hustle the school bully Carl out of a few thousand dollars by confusing him about what discount to apply to a diamond ring he’s selling while working in his Dad’s jewellery store.

## Determining the Discount – Wrong Procedure

In the book, Carl added both of the discounts, giving a total discount of 95%. To find the new price, you subtract the amount that is discounted off of the total price.

*Discount Amount = 95% of $35990*

*Discount Amount = 0.95 × $35990*

*Discount Amount = $34190.5*

*Total Price = $35990 – $34190.5*

*Total Price = $1799.5*

To make it much simpler to calculate, people often just multiply the original amount by the percentage that will be left after the discount.

*Percentage left = 100% – 95%*

*Percentage left = 5%*

*Total Price = 5% of $35990*

*Total Price = 0.05 × $35990*

*Total Price = $1799.5*

## Determining the Discount – Correct Procedure

Carl should have applied the 50% discount first:

*50% of $35990 = $17995*

Then he should have applied the second, 45% discount to that amount. A 45% discount means you are left with 55% of the price:

*55% of $17995 = 0.55 × $17995 = $9897.25*

So the ring *should* have been discounted to **$9897.25**.

Will makes a comment about Carl blowing about eight grand. We can calculate the exact size of his mistake by subtracting the price he sold the ring for from the price he was supposed to use:

*Size of mistake = correct discounted price – price Carl gave*

*Size of mistake = $9897.25 – $1799.5*

*Size of mistake = $8097.75*

No wonder Carl’s dad is annoyed!

## Real Life Example – Deceptive Double Discounts in Store Sales

The double discount is a common tactic used by stores and often results in confusion for buyers. The key to understanding what is happening is to apply the discounts **one after the other**, rather than all at once. Let’s look at a game store closing down sale as an example.

The game store is having a closing down sale, they’ve got a “30% off and then an extra 20% off that” deal going. The game store workers have a (fully functioning) point of sale system to do all the calculations (so no tricking Carl here). Given you’re on a limited budget, how can you find a quick way to calculate the actual cost of an item?

*If you have 30% off, that means you have 70% of the original price.*

*If you have 20% off, it means you have 80% of the original price left (see the pattern?)*

Now the store deal is two discounts applied in order. It will be easier to combine these two together so you only have to do *one* calculation for each item, not two. In this case, the two discount ratios are 70% (100% – 30%) and 80% (100% – 20%):

*new price = discount2 × (discount1 × original price)*

*new price = 80% × (70% × original price)*

*new price = 0.8 × (0.7 × original price)*

*new price = 0.8 × 0.7 × original price*

*new price = 0.56 × original price*

So now you know that the final discounted amount is only 56% of the original price.