- The percent decrease formula is \(\frac{\text{Initial Value} - \text{Final Value}}{\text{Initial Value}} \times 100\%\).
- Option A correctly represents this formula as \(\frac{175-126}{175}\).
- Calculating the value: \(\frac{49}{175} = 0.28\), which is \(28\%\).
- The final answer is \(\boxed{A, 28\%}\).
Explanation
- Identifying the Correct Expression
To determine the percent decrease, we identify the initial quantity as \(175\) and the new quantity as \(126\). The percent decrease measures how much a value has declined relative to its starting value, calculated using the formula:
\[ \text{Percent Decrease} = \frac{\text{Initial Value} - \text{Final Value}}{\text{Initial Value}} \times 100\% \]
Substituting our values into the formula, we have:
\[ \text{Percent Decrease} = \frac{175 - 126}{175} \times 100\% \]
Comparing this to the provided options, we see that it matches option A.
- Calculating the Percent Decrease
Now, we perform the arithmetic calculation to find the specific percent decrease.
First, compute the difference in the numerator:
\[ 175 - 126 = 49 \]
Next, divide this difference by the initial value:
\[ \frac{49}{175} \]
Simplifying the fraction by dividing both numerator and denominator by 7:
\[ \frac{49 \div 7}{175 \div 7} = \frac{7}{25} \]
Finally, convert this fraction to a percentage by multiplying by 100:
\[ \frac{7}{25} \times 100\% = 7 \times 4\% = 28\% \]
Thus, the percent decrease is \(28\%\).
Examples
Percent decrease is frequently used in retail to determine discounts. For example, if a jacket that originally cost \$175 is marked down to \$126, calculating the percent decrease helps customers understand the savings. By using the formula \(\frac{\text{Initial} - \text{New}}{\text{Initial}} \times 100\%\), we find the discount rate is 28%, which is useful for comparing deals across different stores.