Discounts and Taxes

Everyone loves a good great sale.  Have you ever noticed that sale signs are mainly red and yellow?  This is because theses colours are eye-catching and stimulate our emotions.  And most of our shopping is connected to our feelings.  Read more about the psychology of colours here.

Back to discounts.  up to 70% off  That gets  a lot of people excited.  But 70% off does not have a value unless it is 70% off a certain amount.  70% off $100 is $70.  But 70% off $10 is only $7.  Regardless, that 70% off means that you are paying a mere 30% of the original price only.

What if there is an additional discount?  Like 70% off and an additional 50% off?  To an untrained mathematician, this looks like a deal that is beyond good – “it’s more than free.  They may have to give me back some money!”  Uh-uh.  There’s no such thing.  It’s like the Double Sunglasses problem from Dan Meyer’s 3-Act Math Task. He’d be blind if the sunglasses completely blocked his vision.  

So, if it’s not 120% off, then what is the combined discount worth?  Let’s see.  The 70% off means you are paying 30% of the price.  The additional 50% off is off that 30%, making it 15% off.  So the combined discount is really 85% (70% + 15%) off, and not 120% off.

How about an item that is on sale for 60% off and the taxes are 15%, does this mean that you’re only getting a discount of 45%?  That seems like a ripoff.  Here’s really what happens.  So, you get 60% off an item, which means you pay 40% of the regular price.  The tax is applied onto the 40%.  So that’s 15% of the 40%, which is 6%.  In the end, you are getting a 56% discount.

And there you have it, a lesson in discounts and taxes.


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