The owner of a small store buys coats for ​$60.00 each. Answer parts a and b.

Question

Question content area bottom
Part 1
a. He sells the coats for ​$96.00 each. What percent of the purchase price is the sale​ price?
The sale price is
  
160​% 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 ​$45 and sells them. How many jackets must the owner buy for the total jacket sales to be at least ​$250​? Explain your answer.
The owner must buy
  
4 ​jacket(s).
Part 3
Explain your answer.
He sells the jackets for
  
enter your response here​% of ​$45​, or ​$
  
enter your response here.
▼
equals
  
enter your response here. He can only sell a whole number of​ jackets, so he needs to sell
  
enter your response here.
​(Round to two decimal places as​ needed.)

Answer 1

Part 1

a. The sale price of the coat is $96.00, and the purchase price is $60.00. To find what percent of the purchase price the sale price is, you can use the formula:

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

Calculating it:

\[ \text{Percent of Purchase Price} = \left( \frac{96.00}{60.00} \right) \times 100 = 1.6 \times 100 = 160% \]

Thus, the sale price is 160% of the purchase price.

Part 2

b. The owner increased the sale price of the jackets by 160%. The purchase price of the jackets is $45. To calculate the new sale price:

\[ \text{Increased Sale Price} = \text{Purchase Price} + \left( \frac{160}{100} \times \text{Purchase Price} \right) = 45 + (1.6 \times 45) = 45 + 72 = 117 \]

Now, we want to find how many jackets must be sold to earn at least $250 in total sales:

Let \( n \) be the number of jackets sold:

\[ n \times \text{Increased Sale Price} \geq 250 \]

Substituting in the increased sale price we calculated:

\[ n \times 117 \geq 250 \]

Now, divide both sides by 117 to find \( n \):

\[ n \geq \frac{250}{117} \approx 2.14 \]

Since the owner can only sell whole jackets, we round up to the nearest whole number.

Thus, \( n = 3 \) jackets must be sold. So the owner must buy at least 3 jackets to sell at least $250.

Part 3

To explain the answer, after an increase of 160%, he sells the jackets for:

\[ \text{Selling Price} = 117 \]

To check this:

\[ \text{Selling Price} = \text{Purchase Price} + 160% \text{ of the Purchase Price} = 45 + 72 = 117 \]

Next, we need the total sales to be at least $250:

\[ 3 \text{ jackets} \times 117 = 351 \]

Since selling 3 jackets meets the requirement of at least $250 in total sales, he can sell these jackets at the price of $117 each to reach a total of $351 in sales.

So, he needs to sell at least 3 jackets to achieve at least $250 in sales.