To solve this problem, let's break it down into clear steps. We need to find the selling price and the cost of the item, given the markup rate and the markup amount.
1. Understand the Given Information:
- Markup rate: [tex]\(15\%\)[/tex] (or [tex]\(0.15\)[/tex] as a decimal)
- Markup amount: [tex]\(\$260\)[/tex]
2. Relation Between Selling Price, Cost, and Markup Amount:
- Selling Price = Cost + Markup Amount
- Markup Rate = [tex]\(\frac{\text{Markup Amount}}{\text{Selling Price}}\)[/tex]
3. Find the Selling Price:
- We know the formula for the markup rate:
[tex]\[
\text{Markup Rate} = \frac{\text{Markup Amount}}{\text{Selling Price}}
\][/tex]
- Rearranging the formula to solve for the selling price gives us:
[tex]\[
\text{Selling Price} = \frac{\text{Markup Amount}}{\text{Markup Rate}}
\][/tex]
- Substituting the given values:
[tex]\[
\text{Selling Price} = \frac{260}{0.15}
\][/tex]
- Calculate the selling price:
[tex]\[
\text{Selling Price} = 1733.33\ (\text{Rounded to the nearest cent})
\][/tex]
4. Calculate the Cost:
- From the relationship:
[tex]\[
\text{Cost} = \text{Selling Price} - \text{Markup Amount}
\][/tex]
- Using the selling price we found:
[tex]\[
\text{Cost} = 1733.33 - 260
\][/tex]
- Calculate the cost:
[tex]\[
\text{Cost} = 1473.33
\][/tex]
Therefore, the selling price is [tex]\(\$ 1733.33\)[/tex] and the cost is [tex]\(\$ 1473.33\)[/tex].
- Final Answers:
- Selling Price: [tex]\(\$ 1733.33\)[/tex]
- Cost: [tex]\(\$ 1473.33\)[/tex]
