Question
A shopper seeking a bargain combined a 25% off coupon and brought enough money to cover 25% of the base price. Why did this shopper go home disappointed?
Answers
GPT-4o mini
The shopper likely went home disappointed because the combination of the 25% off coupon and having enough money to cover 25% of the base price was not sufficient to make the purchase.
Let's break it down:
1. **Base Price**: Let's denote the base price of the item as \( P \).
2. **25% Off Coupon**: The coupon applies a 25% discount to the base price, which reduces the price to \( 0.75P \) (since 100% - 25% = 75%, or 0.75).
3. **Money Available**: The shopper brought enough money to cover 25% of the base price, which amounts to \( 0.25P \).
Now, let's compare the effective price after the coupon to the amount the shopper has:
- After the coupon, the effective price of the item is \( 0.75P \).
- The shopper only has \( 0.25P \).
Since \( 0.25P \) (the shopper's money) is less than \( 0.75P \) (the discounted price), the shopper does not have enough money to buy the item after applying the coupon.
Thus, despite the discount, the shopper could not afford the item and went home disappointed.
Let's break it down:
1. **Base Price**: Let's denote the base price of the item as \( P \).
2. **25% Off Coupon**: The coupon applies a 25% discount to the base price, which reduces the price to \( 0.75P \) (since 100% - 25% = 75%, or 0.75).
3. **Money Available**: The shopper brought enough money to cover 25% of the base price, which amounts to \( 0.25P \).
Now, let's compare the effective price after the coupon to the amount the shopper has:
- After the coupon, the effective price of the item is \( 0.75P \).
- The shopper only has \( 0.25P \).
Since \( 0.25P \) (the shopper's money) is less than \( 0.75P \) (the discounted price), the shopper does not have enough money to buy the item after applying the coupon.
Thus, despite the discount, the shopper could not afford the item and went home disappointed.