Question
after the start of a new year a $2,560 television set was marked down to $2,048 what was the percent decrease in the price given answer 25%
what error is present in this calculation?
what error is present in this calculation?
Answers
GPT-4o mini
To check the error in the calculation of the percent decrease from $2,560 to $2,048, we can use the formula for percent decrease:
\[
\text{Percent Decrease} = \left( \frac{\text{Original Price} - \text{New Price}}{\text{Original Price}} \right) \times 100
\]
1. **Calculate the difference between the original price and the new price**:
\[
\text{Difference} = 2560 - 2048 = 512
\]
2. **Apply the percent decrease formula**:
\[
\text{Percent Decrease} = \left( \frac{512}{2560} \right) \times 100
\]
3. **Calculate the fraction**:
\[
\frac{512}{2560} = 0.2
\]
4. **Convert to percentage**:
\[
0.2 \times 100 = 20\%
\]
So, the correct percent decrease is **20%**, not 25%.
### Error in Calculation:
The error present in the original calculation is that it incorrectly computed the percent decrease as 25% instead of 20%. This could be due to a miscalculation of the difference, or an error in the application of the percent decrease formula itself.
\[
\text{Percent Decrease} = \left( \frac{\text{Original Price} - \text{New Price}}{\text{Original Price}} \right) \times 100
\]
1. **Calculate the difference between the original price and the new price**:
\[
\text{Difference} = 2560 - 2048 = 512
\]
2. **Apply the percent decrease formula**:
\[
\text{Percent Decrease} = \left( \frac{512}{2560} \right) \times 100
\]
3. **Calculate the fraction**:
\[
\frac{512}{2560} = 0.2
\]
4. **Convert to percentage**:
\[
0.2 \times 100 = 20\%
\]
So, the correct percent decrease is **20%**, not 25%.
### Error in Calculation:
The error present in the original calculation is that it incorrectly computed the percent decrease as 25% instead of 20%. This could be due to a miscalculation of the difference, or an error in the application of the percent decrease formula itself.