To solve the problem of determining which offer is better—two successive discounts of 20% and 10% or a single discount of 30%—we'll calculate the final price after applying each discount method to an initial price. We'll then compare the final prices to find out which one provides a lower price.
Let's assume an initial price of 100 units (this can be dollars, euros, or any other currency). Here are the detailed steps to find the solution:
### Step 1: Apply Two Successive Discounts of 20% and 10%
1. Calculate the first discount (20%):
- Initial price: 100 units
- First discount: [tex]\( 20\% \text{ of } 100 = 0.20 \times 100 = 20 \text{ units} \)[/tex]
- Price after the first discount: [tex]\( 100 - 20 = 80 \text{ units} \)[/tex]
2. Calculate the second discount (10%) on the new price:
- New price after the first discount: 80 units
- Second discount: [tex]\( 10\% \text{ of } 80 = 0.10 \times 80 = 8 \text{ units} \)[/tex]
- Final price after both discounts: [tex]\( 80 - 8 = 72 \text{ units} \)[/tex]
So, the final price after two successive discounts of 20% and 10% is 72 units.
### Step 2: Apply a Single Discount of 30%
1. Calculate the discount (30%):
- Initial price: 100 units
- Discount: [tex]\( 30\% \text{ of } 100 = 0.30 \times 100 = 30 \text{ units} \)[/tex]
- Final price after the discount: [tex]\( 100 - 30 = 70 \text{ units} \)[/tex]
So, the final price after a single discount of 30% is 70 units.
### Step 3: Compare the Final Prices
- Final price after two successive discounts of 20% and 10%: 72 units
- Final price after a single discount of 30%: 70 units
### Conclusion
The single discount of 30% results in a lower final price (70 units) compared to the two successive discounts of 20% and 10% (72 units). Therefore, a single discount of 30% is the better offer.
