To determine whether Lenny and Carol can both be correct, let's analyze the parameters for each of their statements:
1. **Lenny's Statement**:
- The price of the golden crown rounded to the nearest 1000 pounds is 54000 pounds.
- This means the actual price must be within the range that rounds to 54000 when rounded to the nearest 1000.
- This range is from 53500 pounds to 54499 pounds (inclusive).
2. **Carol's Statement**:
- The price of the golden crown rounded to the nearest 10000 pounds is 60000 pounds.
- This means the actual price must be within the range that rounds to 60000 when rounded to the nearest 10000.
- This range is from 55000 pounds to 64999 pounds (inclusive).
Now we need to see if there is any overlap between these two ranges:
- Lenny’s range: 53500 to 54499 pounds.
- Carol’s range: 55000 to 64999 pounds.
These two ranges do not overlap.
Therefore, they cannot both be correct because there is no single price that lies within both given ranges. Thus, it is impossible for both Lenny's and Carol's statements to be accurate simultaneously based on their rounding criteria.
Lenny says the price of a golden crown rounded to the nearest 1000 pounds is 54000 pounds.
Carol says the price of the golden crown rounded to the nearest 10000 pounds is 60000 pounds.
Can they both be correct? Explain your answer.
1 answer