On a market day, Abdul has 32 goats while Chebet has 56 goats. Chebet sold twice as many goats as Abdul. After the sale, the number of goats that Abdul and Chebet remained with was in the ratio 3:5 respectively. Determine the total number of goats sold by Abdul and Chebet in the market.

Part (a)

Step 1: Calculate the number of goats sold by Abdul.
$Goats sold by Abdul = 12 - 6 = 6 goats$

Step 2: Calculate the number of goats sold by Chebet.
$Goats sold by Chebet = 2 \times 6 = 12 goats$

Step 3: Calculate the total number of goats sold.
$Total goats sold = 6 + 12 = 18 goats$

18

Part (b)

Step 1: Let the earnings of Abdul be $3k$ Ksh and Chebet be $5k$ Ksh (ratio 3:5).
Total earnings:
$3k + 5k = 9600$
$8k = 9600$
$k = \frac{9600}{8} = 1200 Ksh$

Step 2: Earnings of Abdul:
$3 \times 1200 = 3600 Ksh$

Step 3: Earnings of Chebet:
$5 \times 1200 = 6000 Ksh$

Step 4: Selling price per goat for Abdul:
$P_A = \frac{3600}{6} = 600 Ksh/goat$

Step 5: Selling price per goat for Chebet:
$P_C = \frac{6000}{12} = 500 Ksh/goat$

Step 6: Ratio of selling prices $P_A : P_C$:
$600 : 500$
Divide by 100:
$6 : 5$

Alternatively:
$\frac{P_A}{P_C} = \frac{earnings_A / goats_A}{earnings_C / goats_C} = \frac{3/5}{6/12} = \frac{3}{5} \times \frac{12}{6} = \frac{3}{5} \times 2 = \frac{6}{5}$

6:5

Part (c)

Step 1: Original selling price per goat by Abdul:
$600 Ksh/goat$

Step 2: New selling price (ratio 19:21 means new:old = 19:21):
$New price = \frac{19}{21} \times 600$
First,
$\frac{600}{21} = \frac{600 \div 3}{21 \div 3} = \frac{200}{7}$
Then,
$\frac{19}{21} \times 600 = 19 \times \frac{200}{7} = \frac{3800}{7} Ksh/goat$

\dfrac{3800{7}}