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Question

Part 1
The owner of a small store buys coats for ​$60.00 each. Answer parts a and b.
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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.
▼
160 divided by 250
250 divided by 45
250 times 160
250 divided by 160
160 divided by 72
250 divided by 72
250 times 72
250 times 45
160 times 45
160 times 72
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.)
The sale price is% of the purchase price.The owner must buyjacket(s).He sells the jackets for45% of $45, or $..jacket(s).HeheHe can only sell a whole number of jackets, so he needs to sell(Round to two decimal places as needed.)

Answer 1

Part 1

a. What percent of the purchase price is the sale price?

To find the percentage of the purchase price that the sale price represents:

1. Sale Price: $96.00
2. Purchase Price: $60.00

The formula to calculate the percentage is:

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

Substituting in the values:

\[ \text{Percentage} = \left( \frac{96}{60} \right) \times 100 = 1.6 \times 100 = 160% \]

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

Part 2

b. The owner increases the sale price by the same percent (160%) when he buys jackets for $45. What is the new sale price?

1. Purchase Price of Jackets: $45.00
2. Percent Increase: 160%

To calculate the increased sale price:

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

Substituting in the values:

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

Thus, the owner sells each jacket for $117.00.

How many jackets must the owner buy for the total jacket sales to be at least $250?**

Let \( x \) be the number of jackets sold.

We need to solve the equation:

\[ 117x \geq 250 \]

To find \( x \):

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

Since he can only sell whole jackets, we round up to the next whole number.

Thus, the owner must buy 3 jackets to achieve sales of at least $250.

Part 3

Explanation:

He sells the jackets for 260% of $45, or $117.

To determine how many jackets he must sell to reach at least $250 in sales:

Using the sale price of $117 per jacket, we calculated that he needs to sell 3 jackets (because \( \lceil 2.14 \rceil = 3 \)), as he can only sell whole jackets.

We previously established:

\[ 117 \times 3 = 351 \text{ which is more than } 250. \]

Answers Summary:

The sale price is 160% of the purchase price. The owner must buy 3 jackets. He sells the jackets for $117, and he needs to sell 3 jackets to meet his sales goal.