Question

Calculate the expected cost of a tablecloth that is five times longer and five times wider than a $3.25 napkin.

Answer 1

To find the expected cost of a tablecloth that is five times longer and five times wider than a napkin that costs $3.25, we need to determine the area of both the napkin and the tablecloth.

1. **Assume dimensions of the napkin:**
Let the dimensions of the napkin be \(l\) (length) and \(w\) (width). Thus, the area of the napkin is:
\[
\text{Area of napkin} = l \times w
\]

2. **Dimensions of the tablecloth:**
Since the tablecloth is five times longer and five times wider, its dimensions will be:
- Length \( = 5l\)
- Width \( = 5w\)

3. **Calculate the area of the tablecloth:**
Thus, the area of the tablecloth is:
\[
\text{Area of tablecloth} = (5l) \times (5w) = 25lw
\]

4. **Compare the areas:**
The area of the tablecloth (25lw) is 25 times that of the napkin (lw):
\[
\text{Area of tablecloth} = 25 \times (\text{Area of napkin})
\]

5. **Calculate the cost of the tablecloth:**
If the cost of the napkin is $3.25, and the cost is proportional to the area, then the cost of the tablecloth will be:
\[
\text{Cost of tablecloth} = 25 \times \text{Cost of napkin} = 25 \times 3.25
\]

6. **Calculate:**
\[
25 \times 3.25 = 81.25
\]

Thus, the expected cost of the tablecloth is **$81.25**.