This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — 24. Sharing Money and Profit a) How much was shared among the five business women? Step 1: Let the total amount shared be T. Jane's share is (3)/(8) of the total amount. Jane's share = (3)/(8) T Step 2: Calculate the remainder after Jane's share. Remainder = T - (3)/(8) T = (5)/(8) T Step 3: Jepchoge's share is (2)/(5) of the remainder. Jepchoge's share = (2)/(5) × ((5)/(8) T) = (2)/(8) T = (1)/(4) T Step 4: Calculate the amount remaining after Jane and Jepchoge's shares. This amount was shared equally among Esther, Mama Charo, and Chepkoech. Remaining amount = (5)/(8) T - (1)/(4) T = (5)/(8) T - (2)/(8) T = (3)/(8) T Step 5: Esther, Mama Charo, and Chepkoech each received Kshs. 6,000. The total amount received by these three is: 3 × Kshs. 6,000 = Kshs. 18,000 Step 6: Equate the remaining fraction of the total amount to the known amount. (3)/(8) T = Kshs. 18,000 Step 7: Solve for T. T = Kshs. 18,000 × (8)/(3) T = Kshs. 6,000 × 8 T = Kshs. 48,000 The total amount shared among the five business women was Kshs. 48,000. Kshs. 48,000 b) How much did Jepchoge get? Step 1: Use the fraction for Jepchoge's share from part (a) and the total amount T. Jepchoge's share = (1)/(4) T Jepchoge's share = (1)/(4) × Kshs. 48,000 Jepchoge's share = Kshs. 12,000 Jepchoge got Kshs. 12,000. Kshs. 12,000 c) Jane, Jepchoge and Chepkoech invested their money and earned a profit of Kshs. 12,000. A third of the profit was left to maintain the business and the rest was shared according to their investments. Find how much each got. Step 1: Determine the initial investments of Jane, Jepchoge, and Chepkoech. Jane's investment: (3)/(8) × Kshs. 48,000 = Kshs. 18,000 Jepchoge's investment: Kshs. 12,000 (from part b) Chepkoech's investment: Kshs. 6,000 (given in the problem) Step 2: Calculate the total profit to be shared. Total profit earned = Kshs. 12,000 Amount left for maintenance = (1)/(3) × Kshs. 12,000 = Kshs. 4,000 Profit to be shared = Kshs. 12,000 - Kshs. 4,000 = Kshs. 8,000 Step 3: Determine the ratio of their investments. Jane : Jepchoge : Chepkoech 18,000 : 12,000 : 6,000 Divide by the greatest common divisor (6,000): 3 : 2 : 1 Total ratio parts = 3 + 2 + 1 = 6 Step 4: Calculate each person's share of the profit. Jane's share of profit: (3)/(6) × Kshs. 8,000 = (1)/(2) × Kshs. 8,000 = Kshs. 4,000 Jepchoge's share of profit: (2)/(6) × Kshs. 8,000 = (1)/(3) × Kshs. 8,000 ≈ Kshs. 2,666.67 Chepkoech's share of profit: (1)/(6) × Kshs. 8,000 ≈ Kshs. 1,333.33 Jane got Kshs. 4,000, Jepchoge got Kshs. 2,666.67, and Chepkoech got Kshs. 1,333.33. Jane: Kshs. 4,000, Jepchoge: Kshs. 2,666.67, Chepkoech: Kshs. 1,333.33 Send me the next one 📸