Question

Question content area top
Part 1
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
  
enter your response here ​jacket(s).

Answer 1

To solve the problem, let's break it down into the two parts as specified.

**Part a:**

The purchase price of the coat is $60. The sale price is $96. We want to find what percent the sale price is of the purchase price.

We can calculate this as follows:

\[
\text{Percentage of sale price to purchase price} = \left( \frac{\text{Sale Price}}{\text{Purchase Price}} \right) \times 100
\]

Substituting the values:

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

So, **the answer to part a** is: **160%**.

---

**Part b:**

We found that the sale price is 160% of the purchase price. Now, let's find the new sale price when the owner buys jackets for $45, using that same percentage increase.

If the purchase price of the jacket is $45 and we increase this by 60%:

We first need to calculate what 160% of $45 is:

\[
\text{Sale Price} = 1.6 \times 45
\]

Calculating that:

\[
\text{Sale Price} = 72
\]

Now, we need to determine how many jackets must be sold at this sale price ($72) for the total jacket sales to be at least $250.

We can set up the equation:

\[
72 \times n \geq 250
\]

Where \(n\) is the number of jackets.

Solving for \(n\),

\[
n \geq \frac{250}{72} \approx 3.47
\]

Since \(n\) must be a whole number, we round up to the next integer:

Thus, \(n = 4\).

So, **the owner must buy** **4 jackets**.

In summary:

- Part a: The sale price is **160%** of the purchase price.
- Part b: The owner must buy **4 jackets**.