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A trader received Ksh. 1,305,000 from selling rice. He sold the rice in 75 kg bags at Ksh. 2,900 per bag. How many kilograms of rice were sold?

Mathematics

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1. A shopkeeper received eight million two hundred and forty-six thousand and thirty-five shillings. Which is the correct numeral?

  1. Break down the number into its place values.

    Eight million = 8,000,000
    Two hundred and forty-six thousand = 246,000
    Thirty-five = 35

  2. Add the values together.

    8,000,000+246,000+35=8,246,0358,000,000 + 246,000 + 35 = 8,246,035

    The correct option is A).

    A) Ksh 8,246,035\boxed{\text{A) Ksh } 8,246,035}

    2. A county recorded 5,738,214 seedlings planted. Round this number to the nearest million.

  3. Identify the millions digit and the digit to its right (hundred thousands digit).

    The millions digit is 5. The hundred thousands digit is 7.

  4. Round based on the hundred thousands digit.

    Since 7 is 5 or greater, round up the millions digit.

    5,738,214≈6,000,0005,738,214 \approx 6,000,000

    The correct option is C).

    C) 6,000,000\boxed{\text{C) } 6,000,000}

    3. Find the next number in the sequence: 1,024, 512, 256, 128, ...

  5. Identify the pattern in the sequence.

    Each number is half of the previous number.

    1,024÷2=5121,024 \div 2 = 512 512÷2=256512 \div 2 = 256 256÷2=128256 \div 2 = 128

  6. Apply the pattern to find the next number.

    128÷2=64128 \div 2 = 64

    The correct option is C).

    C) 64\boxed{\text{C) } 64}

    4. What is the smallest number that can be added to 63,475 to make it divisible by 9?

  7. Calculate the sum of the digits of the given number.

    6+3+4+7+5=256 + 3 + 4 + 7 + 5 = 25

  8. Find the next multiple of 9 that is greater than the sum of the digits.

    The multiples of 9 are 9, 18, 27, 36, ...
    The next multiple of 9 after 25 is 27.

  9. Determine the difference.

    27−25=227 - 25 = 2

    The smallest number to add is 2.
    The correct option is B).

    B) 2\boxed{\text{B) } 2}

    5. Three bells ring at intervals of 12 seconds, 18 seconds and 30 seconds. If they ring together at 9:00:00 a.m., after how long will they ring together again?

  10. Find the Least Common Multiple (LCM) of 12, 18, and 30.

    Prime factorization:

    12=22×312 = 2^2 \times 3 18=2×3218 = 2 \times 3^2 30=2×3×530 = 2 \times 3 \times 5

    LCM = 22×32×5=4×9×5=1802^2 \times 3^2 \times 5 = 4 \times 9 \times 5 = 180

  11. Convert the LCM from seconds to minutes.

    180 seconds÷60 seconds/minute=3 minutes180 \text{ seconds} \div 60 \text{ seconds/minute} = 3 \text{ minutes}

    The bells will ring together again after 3 minutes.
    The correct option is C).

    C) 3 minutes\boxed{\text{C) } 3 \text{ minutes}}

    6. The area of a square garden is 2014 m220 \frac{1}{4} \text{ m}^2. Find its perimeter.

  12. Convert the mixed fraction to an improper fraction.

    2014=(20×4)+14=80+14=814 m220 \frac{1}{4} = \frac{(20 \times 4) + 1}{4} = \frac{80 + 1}{4} = \frac{81}{4} \text{ m}^2

  13. Find the side length (ss) of the square using the area formula (A=s2A = s^2).

    s2=814s^2 = \frac{81}{4} s=814=814=92=4.5 ms = \sqrt{\frac{81}{4}} = \frac{\sqrt{81}}{\sqrt{4}} = \frac{9}{2} = 4.5 \text{ m}

  14. Calculate the perimeter (PP) of the square using the formula (P=4sP = 4s).

    P=4×4.5 m=18 mP = 4 \times 4.5 \text{ m} = 18 \text{ m}

    The correct option is A).

    A) 18 m\boxed{\text{A) } 18 \text{ m}}

    7. Solve: 35×x+4=16\frac{3}{5} \times x + 4 = 16.

  15. Subtract 4 from both sides of the equation.

    35x+4−4=16−4\frac{3}{5}x + 4 - 4 = 16 - 4 35x=12\frac{3}{5}x = 12

  16. Multiply both sides by 5.

    3x=12×53x = 12 \times 5 3x=603x = 60

  17. Divide both sides by 3.

    3x3=603\frac{3x}{3} = \frac{60}{3} x=20x = 20

    The correct option is B).

    B) 20\boxed{\text{B) } 20}

    8. A trader received Ksh. 1,305,000 from selling rice. He sold the rice in 75 kg bags at Ksh. 2,900 per bag. How many kilograms of rice were sold?

  18. Calculate the number of bags sold.

    Number of bags=Total amount receivedPrice per bag\text{Number of bags} = \frac{\text{Total amount received}}{\text{Price per bag}} Number of bags=1,305,000 Ksh2,900 Ksh/bag=450 bags\text{Number of bags} = \frac{1,305,000 \text{ Ksh}}{2,900 \text{ Ksh/bag}} = 450 \text{ bags}

  19. Calculate the total kilograms of rice sold.

    Total kilograms=Number of bags×Kilograms per bag\text{Total kilograms} = \text{Number of bags} \times \text{Kilograms per bag} Total kilograms=450 bags×75 kg/bag=33,750 kg\text{Total kilograms} = 450 \text{ bags} \times 75 \text{ kg/bag} = 33,750 \text{ kg}

    The correct option is B).

    B) 33,750 kg\boxed{\text{B) } 33,750 \text{ kg}}
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