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13. Toby's Cycle Shop advertises a [tex]30\%[/tex] markdown on an Alpine mountain bike regularly priced at [tex]\[tex]$450[/tex]. Cycle City's regular selling price for the same model of bike is [tex]\$[/tex]430[/tex].

a) What is the reduced price at Toby's?

b) What rate of markdown would Cycle City have to offer to match Toby's reduced price?

Sagot :

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.