A department store marked down all of its summer clothing 29%. The following week the remaining items were marked down again 15% off the sale price. When Jorge bought two tank tops on sale, he presented a coupon that gave him an additional 21% off. What percent of the original price did Jorge save?
How would I set this up to solve?
To set up this problem, we will first calculate the total discount for each step and then find out the total percentage of the original price that Jorge saved.
Step 1: Summer clothing marked down 29%
This means the clothing is now sold at 100% - 29% = 71% of the original price.
Step 2: Further discount of 15%
Since the clothing is already discounted to 71%, the further discount will reduce the price to 71% - 15% = 56.35% of the original price.
Step 3: Coupon discount of 21%
Applying the coupon will give an additional discount of 21% off the price of 56.35%.
To calculate this discount, we multiply 56.35% by (100% - 21%), or 0.5635 * 0.79 = 44.4965%.
Now, we can find out what percent of the original price Jorge paid by subtracting the overall discount, 44.4965%, from 100%: 100% - 44.4965% = 55.5035%
Therefore, Jorge saved approximately 55.5035% of the original price.
To solve this problem, we can follow a step-by-step approach:
1. Start by finding the sale price after the first markdown of 29%.
- Subtract 29% from 100% (100% - 29% = 71%).
- This means that the summer clothing is now priced at 71% of its original price.
2. Calculate the sale price after the second markdown of 15% off the sale price.
- Subtract 15% from 100% (100% - 15% = 85%).
- Multiply this percentage by the sale price after the first markdown (71%).
- This will give you the final sale price after both markdowns.
3. Apply the additional discount of 21% when Jorge presents his coupon.
- Subtract 21% from 100% (100% - 21% = 79%).
- Multiply this percentage by the final sale price calculated in the previous step.
- This will give you the price that Jorge actually pays.
4. Calculate the percent of the original price that Jorge saved.
- Divide the price that Jorge paid by the original price (before any markdowns or discounts).
- Multiply the result by 100 to convert it to a percentage.
Let's go through an example calculation to illustrate:
Suppose the original price of the tank tops is $50.
1. Sale price after the first markdown:
Sale Price = $50 * 71% = $35.50
2. Sale price after the second markdown:
Sale Price = $35.50 * 85% = $30.18
3. Price after additional discount with the coupon:
Price after discount = $30.18 * 79% = $23.84
4. Percent saved:
Percent Saved = ($50 - $23.84) / $50 * 100% = 52.32%
Therefore, Jorge saved approximately 52.32% of the original price.
(1-.29)(1-.15)(1-.21) = .71 * .85 * .79 = .476
That is the amount paid at the end,
so the final discount is 1-.476 = 52.4%