 # You are at the store and the price of your goods costs 100. You have two coupons that you can use \$30 off the price of your goods or 15% off the price of your goods. Which is better?

<--- Total Price of Goods before discount
<--- Dollar Amount off
%<--- Percentage Amount off

You are at the store and the price of your goods costs 100. You have two coupons that you can use:
• \$30 off the price of your goods
• 15 percent off the price of your goods
Which coupon yields the better value?

## Calculate Dollar off Price denoted as Pd:

Pd = Price - Dollar off
Pd = \$100.00 - \$30.00
Pd = \$70.00

## Calculate Percentage off Price denoted as Pp:

 Discount Percentage  = 15 100

Discount Percentage = 0.15

If the discount is x%, that means you only pay for (1 - x)% of the price, shown below
Pp = Price x (1 - Discount Percentage)
Pp = 100 x (1 - 0.15)
Pp = 100 x (0.85)
Pp = \$85.00

In this case, the dollar discount of 30 is better than 15% off, so you would use the dollar coupon

## Project the price where the percentage discount beats the dollar discount:

In other words, we need to know when 15% x Price ≥ 30
From above, 15% = 0.15

## Divide each side of the equation by 0.15

 0.15 x Price 0.15
 ≥
 30 0.15

## Cancelling 0.15 from the left side of the equation to solve for price, we get:

 Price  = 30 0.15

Projected Price ≥ \$200.00

This means that if you buy more than \$200.00 of goods, the percentage coupon will reign supreme!

Projected Price ≥ \$200.00

### How does the Coupon Comparison Calculator work?

Given a cost of goods, a dollar off coupon, and a percentage off coupon, this calculator will compare the two deals and determine which one is of more value. If the dollar coupon wins, the calculator will project the break even price where the dollar coupon would surpass the percentage coupon
This calculator has 3 inputs.

### What 1 formula is used for the Coupon Comparison Calculator?

1. Discount Price = Price x (1 - Discount Percentage)

For more math formulas, check out our Formula Dossier

### What 5 concepts are covered in the Coupon Comparison Calculator?

compare
estimate, measure, or note the similarity or difference between
coupon
the annual interest rate paid on a bond, expressed as a percentage of the face value and paid from issue date until maturity.
discount
the amount by which the market price of a bond is lower than its principal amount due at maturity
dollar
Currency unit
percent
a specified amount in or for every hundred. one part in every hundred.
n% = n/100