Certainly! Let's break down the problem into two parts: calculating the cost of each person's portion of the bill, and finding the perimeter and area of rectangles.
### Part 1: Cost of Each Person's Portion
The total cost of the meal is given by the expression [tex]\(48x + 28\)[/tex].
If four people are splitting the bill evenly, we divide the total cost by 4:
[tex]\[
\text{Cost per person} = \frac{48x + 28}{4}
\][/tex]
To simplify this expression:
1. Distribute the division across the terms in the numerator:
[tex]\[
\frac{48x}{4} + \frac{28}{4}
\][/tex]
2. Simplify each term:
[tex]\[
\frac{48x}{4} = 12x
\][/tex]
[tex]\[
\frac{28}{4} = 7
\][/tex]
Therefore, the simplified expression for each person's portion of the bill is:
[tex]\[
12x + 7
\][/tex]
### Part 2: Perimeter and Area of Rectangles
#### Rectangle 1:
- Length: [tex]\( l_1 \)[/tex]
- Width: [tex]\( w_1 \)[/tex]
Perimeter (P) of a rectangle is calculated using the formula:
[tex]\[
P = 2 \times ( \text{length} + \text{width} ) = 2 \times ( l_1 + w_1 )
\][/tex]
Area (A) of a rectangle is calculated using the formula:
[tex]\[
A = \text{length} \times \text{width} = l_1 \times w_1
\][/tex]
#### Rectangle 2:
- Length: [tex]\( l_2 \)[/tex]
- Width: [tex]\( w_2 \)[/tex]
Perimeter:
[tex]\[
P = 2 \times ( l_2 + w_2 )
\][/tex]
Area:
[tex]\[
A = l_2 \times w_2
\][/tex]
#### Rectangle 3:
- Length: [tex]\( l_3 \)[/tex]
- Width: [tex]\( w_3 \)[/tex]
Perimeter:
[tex]\[
P = 2 \times ( l_3 + w_3 )
\][/tex]
Area:
[tex]\[
A = l_3 \times w_3
\][/tex]
Let's summarize the simplified expressions:
1. Cost per person of the meal: [tex]\( 12x + 7 \)[/tex]
2. Perimeter and Area of each rectangle:
- Rectangle 1:
- Perimeter: [tex]\( 2 \times ( l_1 + w_1 ) \)[/tex]
- Area: [tex]\( l_1 \times w_1 \)[/tex]
- Rectangle 2:
- Perimeter: [tex]\( 2 \times ( l_2 + w_2 ) \)[/tex]
- Area: [tex]\( l_2 \times w_2 \)[/tex]
- Rectangle 3:
- Perimeter: [tex]\( 2 \times ( l_3 + w_3 ) \)[/tex]
- Area: [tex]\( l_3 \times w_3 \)[/tex]
That completes our detailed, step-by-step solution to the problem!
