Calculate the fraction of the farm given to the wife and the first child.

Let T be the total acres of the cocoa farm. Step 1: Calculate the fraction of the farm given to the wife and the first child. The wife received (2)/(5) of the acres. The first child received (1)/(3) of the acres. The combined fraction received by the wife and the first child is: (2)/(5) + (1)/(3) = (2 × 3)/(5 × 3) + (1 × 5)/(3 × 5) = (6)/(15) + (5)/(15) = (11)/(15) Step 2: Calculate the fraction of the farm remaining for the other three children. The remaining fraction of the farm is 1 - (11)/(15): 1 - (11)/(15) = (15)/(15) - (11)/(15) = (4)/(15) This (4)/(15) of the total farm was shared among the three children in the ratio 3:5:2. Step 3: Determine the total parts in the ratio and the value of one part. The sum of the ratio parts is 3 + 5 + 2 = 10 parts. The child who had the least share corresponds to the smallest part in the ratio, which is 2 parts. We are given that the child with the least share received 8 acres. So, 2 parts = 8 acres. Therefore, 1 part = 8 acres2 = 4 acres. Step 4: Calculate the total acres shared among the three children. The total acres shared among the three children is 10 parts: Total acres for three children = 10 × 4 acres = 40 acres. Step 5: Calculate the total acres of the farm (T). We know that the 40 acres represents (4)/(15) of the total farm T. (4)/(15) T = 40 acres To find T, multiply both sides by (15)/(4): T = 40 × (15)/(4) T = 10 × 15 T = 150 acres i) The total acres of the man left (meaning the total acres of the farm) is 150 acres. Step 6: Calculate the number of acres the wife received. The wife received (2)/(5) of the total acres T. Wife's acres = (2)/(5) × 150 acres Wife's acres = 2 × (150)/(5) acres Wife's acres = 2 × 30 acres Wife's acres = 60 acres ii) The number of acres the wife received is 60 acres.