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Three friends, Amina, Brian, and Chebet, invest in a business in the ratio 3:5:2. They make a profit of 12,000 shillings. How much does each person receive? Also, how many kilograms of maize flour wer

Mathematics

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Part a· 2 steps

How many kilograms of maize flour were used?

  1. Set up the ratio for maize flour to millet.

    The ratio of maize flour to millet is 5:35:3.
    We are given that 24 kg24 \text{ kg} of millet were used. Let MM be the amount of maize flour used.

    M24 kg=53\frac{M}{24 \text{ kg}} = \frac{5}{3}
  2. Solve for MM.

    M=53×24 kgM = \frac{5}{3} \times 24 \text{ kg} M=5×8 kgM = 5 \times 8 \text{ kg} M=40 kgM = 40 \text{ kg}

    The amount of maize flour used was 40 kg\boxed{\text{40 kg}}.

Part b· 6 steps

If the school wants to prepare enough porridge for twice as many students, how much maize flour and millet will be used?

  1. Determine the new amounts needed for twice as many students.

    To prepare for twice as many students, the amount of each ingredient must be doubled.
    From part (a), maize flour used was 40 kg40 \text{ kg} and millet used was 24 kg24 \text{ kg}.

  2. Calculate the new amounts of maize flour and millet.

    New maize flour needed:

    2×40 kg=80 kg2 \times 40 \text{ kg} = 80 \text{ kg}

    New millet needed:

    2×24 kg=48 kg2 \times 24 \text{ kg} = 48 \text{ kg}

    For twice as many students, the school will use 80 kg of maize flour and 48 kg of millet\boxed{\text{80 kg of maize flour and 48 kg of millet}}.

    :
    Three friends, Amina, Brian, and Chebet, invest in a business in the ratio 3:5:23:5:2. They make a profit of 12,000 shillings. How much does each person receive?

  3. Calculate the total number of ratio parts.

    The investment ratio is Amina : Brian : Chebet = 3:5:23:5:2.
    Total parts = 3+5+2=103 + 5 + 2 = 10 parts.

  4. Calculate Amina's share of the profit.

    Amina's share = Amina’s ratio partTotal ratio parts×Total profit\frac{\text{Amina's ratio part}}{\text{Total ratio parts}} \times \text{Total profit}

    Amina’s share=310×12,000 shillings\text{Amina's share} = \frac{3}{10} \times 12,000 \text{ shillings} Amina’s share=3×1,200 shillings=3,600 shillings\text{Amina's share} = 3 \times 1,200 \text{ shillings} = 3,600 \text{ shillings}
  5. Calculate Brian's share of the profit.

    Brian's share = Brian’s ratio partTotal ratio parts×Total profit\frac{\text{Brian's ratio part}}{\text{Total ratio parts}} \times \text{Total profit}

    Brian’s share=510×12,000 shillings\text{Brian's share} = \frac{5}{10} \times 12,000 \text{ shillings} Brian’s share=5×1,200 shillings=6,000 shillings\text{Brian's share} = 5 \times 1,200 \text{ shillings} = 6,000 \text{ shillings}
  6. Calculate Chebet's share of the profit.

    Chebet's share = Chebet’s ratio partTotal ratio parts×Total profit\frac{\text{Chebet's ratio part}}{\text{Total ratio parts}} \times \text{Total profit}

    Chebet’s share=210×12,000 shillings\text{Chebet's share} = \frac{2}{10} \times 12,000 \text{ shillings} Chebet’s share=2×1,200 shillings=2,400 shillings\text{Chebet's share} = 2 \times 1,200 \text{ shillings} = 2,400 \text{ shillings}

    Amina receives 3,600 shillings\boxed{\text{3,600 shillings}}, Brian receives 6,000 shillings\boxed{\text{6,000 shillings}}, and Chebet receives 2,400 shillings\boxed{\text{2,400 shillings}}.

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