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.
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