The owner of a small store buys coats for ​$40.00 each. Answer parts a and b.

Question

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Part 1
a. He sells the coats for ​$72.00 each. What percent of the purchase price is the sale​ price?
The sale price is
  
180​% of the purchase price.
Part 2
b. The owner increases the sale price by the same percent that you found in part a when he buys jackets for ​$25 and sells them. How many jackets must the owner buy for the total jacket sales to be at least ​$260​? Explain your answer.
The owner must buy
  
enter your response here ​jacket(s).

Answer 1

To solve the problem, we'll tackle each part step by step.

Part 1: Finding the Sale Price as a Percentage of the Purchase Price

1. Calculate the sale price percentage relative to the purchase price.

   • Purchase Price of Coat = $40.00
   • Sale Price of Coat = $72.00

   To find what percent the sale price is of the purchase price:

   \[ \text{Percentage} = \left( \frac{\text{Sale Price}}{\text{Purchase Price}} \right) \times 100 \]

   Substituting the values:

   \[ \text{Percentage} = \left( \frac{72}{40} \right) \times 100 = 1.8 \times 100 = 180% \]

   The sale price is 180% of the purchase price.

Part 2: Jacket Sales

1. Determine the increase percentage based on the coats' pricing.

   • Since we found that the sale price of the coats is 180% of the purchase price, that means the increase is 80% of the purchase price (because 180% - 100% = 80%).

2. Calculate the increased sale price for the jackets.

   • Purchase Price of Jacket = $25.00
   • Increase = 80% of $25.00

   First, calculate 80% of $25.00:

   \[ \text{Increase} = 0.80 \times 25 = 20 \]

   Now, we find the new sale price of the jackets:

   \[ \text{New Sale Price} = \text{Purchase Price} + \text{Increase} = 25 + 20 = 45 \]

   So, the sale price of the jackets is $45.00 each.

3. Determine how many jackets are needed to achieve at least $260 in sales.

   To find out how many jackets the owner must sell to reach at least $260:

   \[ \text{Number of Jackets} = \left\lceil \frac{\text{Total Sales Goal}}{\text{Sale Price per Jacket}} \right\rceil \]

   Substituting in the values:

   \[ \text{Number of Jackets} = \left\lceil \frac{260}{45} \right\rceil \approx \left\lceil 5.78 \right\rceil \]

   Hence, rounding up, the owner needs to sell 6 jackets to at least meet the sales goal of $260.

Final Answers

Part 1: The sale price is 180% of the purchase price.
Part 2: The owner must buy 6 jackets.