Sure, let's solve these problems step-by-step.
a) What is the reduced price at Toby's?
1. Understand the problem:
- Original price at Toby's Cycle Shop: \[tex]$450
- Markdown percentage: \(30\%\)
2. Calculate the amount of the markdown:
The markdown amount can be found by multiplying the original price by the markdown percentage:
\[
\text{Markdown amount} = \text{Original price} \times \left(\frac{\text{Markdown percentage}}{100}\right) = 450 \times \left(\frac{30}{100}\right)
\]
3. Calculate the markdown amount:
\[
\text{Markdown amount} = 450 \times 0.30 = 135
\]
4. Subtract the markdown amount from the original price:
\[
\text{Reduced price} = \text{Original price} - \text{Markdown amount} = 450 - 135 = 315
\]
So, the reduced price at Toby's is \$[/tex]315.
b) What rate of markdown would Cycle City have to offer to match Toby's reduced price?
1. Understand the problem:
- Regular price at Cycle City: \[tex]$430
- Target reduced price to match Toby's: \$[/tex]315
2. Calculate the markdown amount needed at Cycle City:
[tex]\[
\text{Markdown amount needed} = \text{Regular price at Cycle City} - \text{Target reduced price} = 430 - 315
\][/tex]
3. Calculate the markdown amount:
[tex]\[
\text{Markdown amount needed} = 115
\][/tex]
4. Calculate the markdown percentage:
Use the markdown amount and the regular price at Cycle City to find the percentage:
[tex]\[
\text{Markdown percentage} = \left(\frac{\text{Markdown amount}}{\text{Regular price at Cycle City}}\right) \times 100 = \left(\frac{115}{430}\right) \times 100
\][/tex]
5. Calculate the markdown percentage:
[tex]\[
\text{Markdown percentage} \approx 26.74\%
\][/tex]
So, Cycle City would have to offer a markdown of approximately 26.74% to match Toby's reduced price.
