Question
A bookstore decides to divide its space into three rectangular sections, nonfiction, books novels and stationary. The books store wants to default 1/3 of it space stationary if the total bookstore is 288 ft.² in the stationary section 12 feet wide will be the stationary section.
Answers
GPT-4o mini
To divide the bookstore space into three sections—nonfiction, novels, and stationary—let's first determine how much space each section will occupy.
1. **Total Space**: The total space of the bookstore is 288 ft².
2. **Stationary Section**: The bookstore wants to allocate \( \frac{1}{3} \) of its space to the stationary section.
Calculating the area of the stationary section:
\[
\text{Area of stationary section} = \frac{1}{3} \times 288 \, \text{ft}^2 = 96 \, \text{ft}^2
\]
Since the stationary section is given to be 12 feet wide, we can find its length using the formula for the area of a rectangle (Area = Width × Length):
\[
\text{Area} = \text{Width} \times \text{Length}
\]
Substituting the known values into the equation:
\[
96 \, \text{ft}^2 = 12 \, \text{ft} \times \text{Length}
\]
Now, solve for the length:
\[
\text{Length} = \frac{96 \, \text{ft}^2}{12 \, \text{ft}} = 8 \, \text{ft}
\]
So, the stationary section will have dimensions:
- **Width**: 12 ft
- **Length**: 8 ft
3. **Remaining Space**: Since 1/3 of the total area is allocated to the stationary section, the remaining area for nonfiction and novels is:
\[
288 \, \text{ft}^2 - 96 \, \text{ft}^2 = 192 \, \text{ft}^2
\]
Now you can divide the remaining 192 ft² between the nonfiction and novels sections. If you want to divide them equally, each would get:
\[
\text{Area for each remaining section} = \frac{192 \, \text{ft}^2}{2} = 96 \, \text{ft}^2
\]
You can then choose dimensions (width and length) for the nonfiction and novels sections based on their areas.
For example, if both sections have a width of 12 ft as well, each will be:
\[
\text{Length} = \frac{96 \, \text{ft}^2}{12 \, \text{ft}} = 8 \, \text{ft}
\]
Thus the dimensions for each section could be configured as follows:
- **Stationary Section**: 12 ft (width) × 8 ft (length)
- **Nonfiction Section**: 12 ft (width) × 8 ft (length)
- **Novels Section**: 12 ft (width) × 8 ft (length)
This ensures that all three sections together form the total area of the bookstore.
1. **Total Space**: The total space of the bookstore is 288 ft².
2. **Stationary Section**: The bookstore wants to allocate \( \frac{1}{3} \) of its space to the stationary section.
Calculating the area of the stationary section:
\[
\text{Area of stationary section} = \frac{1}{3} \times 288 \, \text{ft}^2 = 96 \, \text{ft}^2
\]
Since the stationary section is given to be 12 feet wide, we can find its length using the formula for the area of a rectangle (Area = Width × Length):
\[
\text{Area} = \text{Width} \times \text{Length}
\]
Substituting the known values into the equation:
\[
96 \, \text{ft}^2 = 12 \, \text{ft} \times \text{Length}
\]
Now, solve for the length:
\[
\text{Length} = \frac{96 \, \text{ft}^2}{12 \, \text{ft}} = 8 \, \text{ft}
\]
So, the stationary section will have dimensions:
- **Width**: 12 ft
- **Length**: 8 ft
3. **Remaining Space**: Since 1/3 of the total area is allocated to the stationary section, the remaining area for nonfiction and novels is:
\[
288 \, \text{ft}^2 - 96 \, \text{ft}^2 = 192 \, \text{ft}^2
\]
Now you can divide the remaining 192 ft² between the nonfiction and novels sections. If you want to divide them equally, each would get:
\[
\text{Area for each remaining section} = \frac{192 \, \text{ft}^2}{2} = 96 \, \text{ft}^2
\]
You can then choose dimensions (width and length) for the nonfiction and novels sections based on their areas.
For example, if both sections have a width of 12 ft as well, each will be:
\[
\text{Length} = \frac{96 \, \text{ft}^2}{12 \, \text{ft}} = 8 \, \text{ft}
\]
Thus the dimensions for each section could be configured as follows:
- **Stationary Section**: 12 ft (width) × 8 ft (length)
- **Nonfiction Section**: 12 ft (width) × 8 ft (length)
- **Novels Section**: 12 ft (width) × 8 ft (length)
This ensures that all three sections together form the total area of the bookstore.