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A total amount of money was shared among five business women. Jane received 3/8 of the total amount. Jepchoge received 2/5 of the remainder. The remaining amount was shared equally among Esther, Mama

Mathematics

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24. Sharing Money and Profit

Part a· 7 steps

How much was shared among the five business women?

  1. Let the total amount shared be TT.

    Jane's share is 38\frac{3}{8} of the total amount.

    Jane’s share=38T\text{Jane's share} = \frac{3}{8} T
  2. Calculate the remainder after Jane's share.

    Remainder=T−38T=58T\text{Remainder} = T - \frac{3}{8} T = \frac{5}{8} T
  3. Jepchoge's share is 25\frac{2}{5} of the remainder.

    Jepchoge’s share=25×(58T)=28T=14T\text{Jepchoge's share} = \frac{2}{5} \times \left(\frac{5}{8} T\right) = \frac{2}{8} T = \frac{1}{4} T
  4. Calculate the amount remaining after Jane and Jepchoge's shares.

    This amount was shared equally among Esther, Mama Charo, and Chepkoech.

    Remaining amount=58T−14T=58T−28T=38T\text{Remaining amount} = \frac{5}{8} T - \frac{1}{4} T = \frac{5}{8} T - \frac{2}{8} T = \frac{3}{8} T
  5. Esther, Mama Charo, and Chepkoech each received Kshs.

    6,000.
    The total amount received by these three is:

    3×Kshs. 6,000=Kshs. 18,0003 \times \text{Kshs. } 6,000 = \text{Kshs. } 18,000
  6. Equate the remaining fraction of the total amount to the known amount.

    38T=Kshs. 18,000\frac{3}{8} T = \text{Kshs. } 18,000
  7. Solve for TT.

    T=Kshs. 18,000×83T = \text{Kshs. } 18,000 \times \frac{8}{3} T=Kshs. 6,000×8T = \text{Kshs. } 6,000 \times 8 T=Kshs. 48,000T = \text{Kshs. } 48,000

    The total amount shared among the five business women was Kshs. 48,000.
    Kshs. 48,000

Part b· 5 steps

How much did Jepchoge get?

  1. Use the fraction for Jepchoge's share from part (a) and the total amount TT.

    Jepchoge’s share=14T\text{Jepchoge's share} = \frac{1}{4} T Jepchoge’s share=14×Kshs. 48,000\text{Jepchoge's share} = \frac{1}{4} \times \text{Kshs. } 48,000 Jepchoge’s share=Kshs. 12,000\text{Jepchoge's share} = \text{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.

  2. Determine the initial investments of Jane, Jepchoge, and Chepkoech.

    Jane's investment: 38×Kshs. 48,000=Kshs. 18,000\frac{3}{8} \times \text{Kshs. } 48,000 = \text{Kshs. } 18,000
    Jepchoge's investment: Kshs. 12,000\text{Kshs. } 12,000 (from part b)
    Chepkoech's investment: Kshs. 6,000\text{Kshs. } 6,000 (given in the problem)

  3. Calculate the total profit to be shared.

    Total profit earned = Kshs. 12,000
    Amount left for maintenance = 13×Kshs. 12,000=Kshs. 4,000\frac{1}{3} \times \text{Kshs. } 12,000 = \text{Kshs. } 4,000
    Profit to be shared = Kshs. 12,000−Kshs. 4,000=Kshs. 8,000\text{Kshs. } 12,000 - \text{Kshs. } 4,000 = \text{Kshs. } 8,000

  4. Determine the ratio of their investments.

    Jane : Jepchoge : Chepkoech

    18,000:12,000:6,00018,000 : 12,000 : 6,000

    Divide by the greatest common divisor (6,000):

    3:2:13 : 2 : 1

    Total ratio parts = 3+2+1=63 + 2 + 1 = 6

  5. Calculate each person's share of the profit.

    Jane's share of profit:

    36×Kshs. 8,000=12×Kshs. 8,000=Kshs. 4,000\frac{3}{6} \times \text{Kshs. } 8,000 = \frac{1}{2} \times \text{Kshs. } 8,000 = \text{Kshs. } 4,000

    Jepchoge's share of profit:

    26×Kshs. 8,000=13×Kshs. 8,000≈Kshs. 2,666.67\frac{2}{6} \times \text{Kshs. } 8,000 = \frac{1}{3} \times \text{Kshs. } 8,000 \approx \text{Kshs. } 2,666.67

    Chepkoech's share of profit:

    16×Kshs. 8,000≈Kshs. 1,333.33\frac{1}{6} \times \text{Kshs. } 8,000 \approx \text{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

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