To determine if Mike's calculation of the percent change using the ratio [tex]$\frac{55}{220} = 25\%$[/tex] is correct, let's go through the problem step-by-step.
1. Identify the usual and sale prices of the bike:
- Usual price: [tex]$275
- Sale price: $[/tex]220
2. Calculate the amount of decrease in price:
- Price decrease = Usual price - Sale price
- Price decrease = [tex]$275 - $[/tex]220 = $55
3. Calculate the percent change using the correct formula:
- Percent change = [tex]\(\left(\frac{\text{Price decrease}}{\text{Usual price}}\right) \times 100\)[/tex]
- Percent change = [tex]\(\left(\frac{55}{275}\right) \times 100\)[/tex]
- Percent change = [tex]\(\left(\frac{1}{5}\right) \times 100\)[/tex]
- Percent change = 20%
4. Mike's calculation:
- Mike used the ratio [tex]\(\frac{55}{220}\)[/tex] to find the percent change.
- Mike's calculation: [tex]\(\left(\frac{55}{220}\right) \times 100 = 25\%\)[/tex]
5. Conclusion:
- The correct percent change should be calculated using the usual price (original price), not the sale price.
- The accurate calculation of the percent change is 20%, not 25%.
Thus, Mike's calculation is incorrect because he used the sale price instead of the usual price to find the percent change. The correct percent change in the price of the bike is 20%.
