The problem has three parts: (a) Factorize the expression $5ay - by + 15a - 3b$. (b) Solve the equation $\frac{6}{4p-1} = \frac{4}{3(p+4)}$. (c) Esi and Kofi shared GH¢21,000.00 in the ratio 2:5. Determine how much more Kofi received than Esi.

1. Problem Description

The problem has three parts:

(a) Factorize the expression $5ay - by + 15a - 3b$.

(b) Solve the equation $\frac{6}{4p-1} = \frac{4}{3(p+4)}$.

(c) Esi and Kofi shared GH¢21,000.00 in the ratio 2:

5. Determine how much more Kofi received than Esi.

2. Solution Steps

(a) Factorization:

We want to factorize $5ay - by + 15a - 3b$.

We can group the terms as follows: $(5ay - by) + (15a - 3b)$.

Now factor out common terms from each group: $y(5a - b) + 3(5a - b)$.

Since both terms have $(5a - b)$ as a factor, we can factor it out: $(5a - b)(y + 3)$.

(b) Solving the equation:

We have $\frac{6}{4p-1} = \frac{4}{3(p+4)}$.

Cross-multiply to get $6 \cdot 3(p+4) = 4(4p-1)$.

$18(p+4) = 16p - 4$

$18p + 72 = 16p - 4$

$18p - 16p = -4 - 72$

$2p = -76$

$p = \frac{-76}{2}$

$p = -38$

(c) Ratio problem:

Total amount = GH¢21,000.00

Ratio of Esi to Kofi = 2:5

Total ratio = 2 + 5 = 7

Esi's share $= \frac{2}{7} \times 21000 = 2 \times 3000 = 6000$

Kofi's share $= \frac{5}{7} \times 21000 = 5 \times 3000 = 15000$

Difference = Kofi's share - Esi's share = 15000 - 6000 = 9000

3. Final Answer

(a) $(5a - b)(y + 3)$

(b) $p = -38$

(c) GH¢9,000.00