# Dueling Discounts

## Arguement

Lets say little Billy wants this cool new Batmobile like the one in example 1 above. Lets say you have the option of using a coupon of 20% off or a coupon of \$20 off. Given the total price of the toy is \$26.99, \$20 off seems like the obvious choice. But for the sake of argument lets do the math and see if the obvious choice is best. To make it easier well round \$26.99 to \$27. 20% of \$27 is \$5.40. Not a really big discount, compared to the second and obvious better choice of \$20 off. \$5.40 minus \$27 is \$22.60. Whereas \$20 minus \$27 is \$7. So in this scenario \$20 off wins.

Looking at the desk (example 2), we have a price of \$99.99. Which most of us would round to \$100. On first glance \$20 might seem like the better deal to most. But doing the math we see in this example both coupons hold the same value. 20% of 100 is 20. Take that \$20 and minus it from the \$100 and we get \$80. Same with the \$20 off coupon, \$20 minus \$100 is \$80. So in some cases the amount of the item itself is the key, not the coupon itself.

The big screen T.V. (example 3), has a price of \$1499.99. Again to make it easier for us we would round to an even \$1500. In this case which coupon to use is at first glance harder to figure out in our heads without stepping back and thinking about it. So what does the math say? Easiest one is the \$20 off coupon. \$1500 minus \$20 is \$1480. Not a very impressive discount. Using the the 20% off coupon, the math says we can save \$300. A far more impressive discount. \$1500 minus \$300 is \$1200. 20% off wins in this scenario.

## What if we had coupons of 5% off and \$5 off?

Using the same examples but with different values for the discounts, lets see if there is any change. In the case of the Batmobile 5% off would give a discount of \$1.35. Still less of a discount of then \$5 off coupon. So in this scenario there is no change.

Looking at the desk, 5% off would get you a discount of \$5. Which is equal to the discount offered by the \$5 off coupon. Once again no change even with different values.

For the t.v. 5% off gives a total savings of \$75. Still far greater a discount the the \$5 off coupon.

## Conclusion

Looking at the three different examples we could easily determine in what scenarios it would be better to use the two different coupons. In this case we could see that items with a value of less than \$100 benefited from the use of a coupon with a x amount of dollars off versus an item with a value greater than \$100, which benefited from a coupon of x amount of percent off. But in the case of an item with value of \$100, the discounts amounted to the same.