To find the percentage by which the price of the sweater was reduced, we can use the formula for percentage decrease:
\[ \text{Percentage Decrease} = \left( \frac{\text{Old Price} - \text{New Price}}{\text{Old Price}} \right) \times 100 \]
In this case:
- Old Price = $20
- New Price = $12
Now, we calculate the decrease in price:
\[ \text{Decrease} = \text{Old Price} - \text{New Price} = 20 - 12 = 8 \]
Next, we can substitute this value back into the percentage decrease formula:
\[ \text{Percentage Decrease} = \left( \frac{8}{20} \right) \times 100 \]
Calculating this:
\[ \frac{8}{20} = 0.4 \] \[ 0.4 \times 100 = 40 \]
Thus, the price of the sweater was reduced by 40%.