Qtn 20: a) Find the dimensions of a rectangle. b) Determine the amount received by each Partner that year.

Let $w$ be the width of the rectangular plot in feet.
Let $l$ be the length of the rectangular plot in feet.

The length exceeds the width by 7 ft:

The area of the plot is 60 sq. ft:

Rearrange into a standard quadratic equation:

We can factor the quadratic equation. We need two numbers that multiply to -60 and add to 7. These numbers are 12 and -5.

This gives two possible solutions for $w$:

Since width cannot be negative, we take $w=5$ ft.

Using $l = w + 7$:

The dimensions of the rectangle are 12 ft by 5 ft.
The final answer for part (a) is $\boxed{\text{Length} = 12 \text{ ft, Width} = 5 \text{ ft}}$.

Wabusi: 300,000
Aisha: 500,000
Wekesa: 700,000
Total Capital ($C$) = $300,000 + 500,000 + 700,000 = 1,500,000$

The profit was one and $\frac{1}{4}$ times the capital:

$\frac{1}{3}$ of the profit was ploughed back:

$\frac{1}{5}$ of the remainder was kept for emergency:

Wabusi : Aisha : Wekesa = $300,000 : 500,000 : 700,000$
Simplify the ratio by dividing by 100,000:
Ratio = $3 : 5 : 7$
Total parts in the ratio = $3 + 5 + 7 = 15$

Wabusi's share = $\frac{3}{15} \times 1,000,000 = \frac{1}{5} \times 1,000,000 = 200,000$
Aisha's share = $\frac{5}{15} \times 1,000,000 = \frac{1}{3} \times 1,000,000 = \frac{1,000,000}{3} \approx 333,333.33$
Wekesa's share = $\frac{7}{15} \times 1,000,000 = \frac{7,000,000}{15} \approx 466,666.67$

The amounts received by each partner are:

• Wabusi: $\boxed{200,000}$
• Aisha: $\boxed{333,333.33}$ (rounded to two decimal places)
• Wekesa: $\boxed{466,666.67}$ (rounded to two decimal places)