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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.

Mathematics

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Answers

3 parts
a
18
b
6:5
c

38007\dfrac{3800}{7}

Step-by-step solution

11 steps

Part a· 3 steps

  1. Calculate the number of goats sold by Abdul.

    Goats sold by Abdul=12−6=6 goats\text{Goats sold by Abdul} = 12 - 6 = 6 \text{ goats}

  2. Calculate the number of goats sold by Chebet.

    Goats sold by Chebet=2×6=12 goats\text{Goats sold by Chebet} = 2 \times 6 = 12 \text{ goats}

  3. Calculate the total number of goats sold.

    Total goats sold=6+12=18 goats\text{Total goats sold} = 6 + 12 = 18 \text{ goats}

    18

Part b6:5

  1. Let the earnings of Abdul be $3k$ Ksh and Chebet be $5k$ Ksh (ratio 3:5).

    Total earnings:

    3k+5k=96003k + 5k = 9600 8k=96008k = 9600 k=96008=1200 Kshk = \frac{9600}{8} = 1200 \text{ Ksh}

  2. Earnings of Abdul

    3×1200=3600 Ksh3 \times 1200 = 3600 \text{ Ksh}

  3. Earnings of Chebet

    5×1200=6000 Ksh5 \times 1200 = 6000 \text{ Ksh}

  4. Selling price per goat for Abdul

    PA=36006=600 Ksh/goatP_A = \frac{3600}{6} = 600 \text{ Ksh/goat}

  5. Selling price per goat for Chebet

    PC=600012=500 Ksh/goatP_C = \frac{6000}{12} = 500 \text{ Ksh/goat}

  6. Ratio of selling prices PA:PCP_A : P_C

    600:500600 : 500

    Divide by 100:

    6:56 : 5

    Alternatively:

    PAPC=earningsA/goatsAearningsC/goatsC=3/56/12=35×126=35×2=65\frac{P_A}{P_C} = \frac{\text{earnings}_A / \text{goats}_A}{\text{earnings}_C / \text{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

38007\dfrac{3800}{7}

  1. Original selling price per goat by Abdul

    600 Ksh/goat600 \text{ Ksh/goat}

  2. New selling price (ratio 19:21 means new:old = 19:21)

    New price=1921×600\text{New price} = \frac{19}{21} \times 600

    First,

    60021=600÷321÷3=2007\frac{600}{21} = \frac{600 \div 3}{21 \div 3} = \frac{200}{7}

    Then,

    1921×600=19×2007=38007 Ksh/goat\frac{19}{21} \times 600 = 19 \times \frac{200}{7} = \frac{3800}{7} \text{ Ksh/goat}

    \dfrac{3800}{7}

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