Discounts

Explanation

We will think of this as a percent-of-decrease problem.  We want to find what percent of the 59.99 USD original price the amount of the discount represents.

Solution

From the advertisement, we see that the original price of the women's shoes is 59.99 USD and the sale price is 33.99 USD.  The discount (decrease in price) is found using subtraction.

• Use the formula: Amount of discount = original price - sale price.
  • 59.99 - 33.99 = 26

The shoes are discounted 26 USD.  Now we find what percent of the original price the 26 USD discount represents.

• This is the amount of the discount formula
  • Amount of discount = discount rate x original price
• Substitute 26 for the amount of discount and 59.99 for the original price.  Let x represent the unknown discount rate.
  • 26 = x ⋅ 59.99
• To undo the multiplication by 59.99 and isolate x on the right side of the equation, divide both sides by 59.99
  • \(\frac{26}{59.99} = \frac{x \cdot 59.99}{59.99}\)
• To simplify the fraction on the right side of the equation, remove the common factor of 59.99 from the numerator and denominator.  On the left side, divide 26 by 59.99.
  • 0.433 ≈ \(\require{cancel} \frac{x \cdot \cancel{59..99}^1}{\cancel{59.99}_1}\)
• To write the decimal 0.433 as a percent, multiply by 100 by moving the decimal point two places to the right, and then insert a % symbol.
  • 043.3% ≈ x
• Round to the nearest one percent.
• 43% ≈ x

To the nearest one percent, the discount rate on the women's shoes is 43%.