Question
The owner of a small store buys coats for $60.00 each. Answer parts a and b.
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.)
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.)
Answers
GPT-4o mini
### 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.
**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.