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\begin{tabular}{l|l} Jo works at a service station and has to reduce the & \( 15 \times 0.5=7.5 \) \\ price of some expired items. Here is his calculation. & \\ By what percentage did he reduce the items? \end{tabular}

Ask by Estrada Herrera. in Australia
Feb 21,2025

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Tutor-Verified Answer

Answer

Jo reduced the price by 50%.

Solution

To find the percentage by which Jo reduced the price of the expired items, we need to calculate the percentage decrease. Given: Original price = \(15\) Reduced price = \(7.5\) The percentage decrease can be calculated using the formula: \[ \text{Percentage decrease} = \left( \frac{\text{Original price} - \text{Reduced price}}{\text{Original price}} \right) \times 100\% \] Substitute the given values into the formula: \[ \text{Percentage decrease} = \left( \frac{15 - 7.5}{15} \right) \times 100\% \] Now, we can calculate the percentage decrease. Calculate the value by following steps: - step0: Calculate: \(\frac{\left(15-7.5\right)}{15}\times 100\) - step1: Remove the parentheses: \(\frac{15-7.5}{15}\times 100\) - step2: Subtract the numbers: \(\frac{7.5}{15}\times 100\) - step3: Divide the terms: \(\frac{1}{2}\times 100\) - step4: Reduce the numbers: \(1\times 50\) - step5: Simplify: \(50\)

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The Deep Dive

To find the percentage reduction, we first need to determine how much Jo reduced the price of the expired items. The original price was \( 15 \) and Jo reduced it to \( 7.5 \). So, the reduction amount is \( 15 - 7.5 = 7.5 \). Now, to calculate the percentage reduction, we use the formula: \[ \text{Percentage Reduction} = \left( \frac{\text{Reduction Amount}}{\text{Original Price}} \right) \times 100 \] Substituting in the values: \[ \text{Percentage Reduction} = \left( \frac{7.5}{15} \right) \times 100 = 50\% \] Jo reduced the price of the items by 50%. --- Did you know that percentages are not just used in retail pricing but also play a crucial role in statistics? For instance, when analyzing survey results, percentages help summarize data, making it easier for businesses to gauge public opinion and make informed decisions. If you ever find yourself needing to calculate percentages quickly, a handy tip is to always remember that 50% means half, 25% means a quarter, and 10% is one-tenth. Making these quick mental calculations can save time, especially when dealing with discounts or sales!

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