To determine whether Mike's calculation of the percent change is correct, let's follow a detailed, step-by-step approach:
1. Identify the original and sale prices:
- Original price of the mountain bike: [tex]$275
- Sale price of the mountain bike: $[/tex]220
2. Calculate the difference in price:
To find the difference, subtract the sale price from the original price:
[tex]\[ 275 - 220 = 55 \][/tex]
So, the price difference is $55.
3. Calculate the percent change:
Percent change is determined by taking the difference in price, dividing it by the original price, and then multiplying by 100 to get a percentage:
[tex]\[ \text{Percent change} = \left( \frac{\text{Price difference}}{\text{Original price}} \right) \times 100 \][/tex]
Substituting the values:
[tex]\[ \text{Percent change} = \left( \frac{55}{275} \right) \times 100 \][/tex]
4. Perform the division:
[tex]\[ \frac{55}{275} = 0.2 \][/tex]
5. Convert to a percentage:
[tex]\[ 0.2 \times 100 = 20 \% \][/tex]
Therefore, the correct percent change is 20%.
Mike is incorrect in his approach because he used the sale price instead of the original price in his calculation. He used the ratio:
[tex]\[ \frac{55}{220} \approx 0.25 \][/tex]
Then he multiplied it by 100, which gave him 25%.
However, the correct procedure is to base the percent change on the original price, not the sale price. Using the original price, the percent change is indeed 20%.
