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LCM of 40; 120; and 200 3. Nyeleti took out a loan of R 80 000.00 from the lender which charges her 15% interest at the end of each year. How much will she owe in 5 years' time?

Mathematics

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5 parts
2.2
600
2.3

R160 908.56R 160\,908.56

3.1
9
3.2
-20
3.3

27−8\sqrt{27} - 8

-2.80

Step-by-step solution

15 steps

Here are the solutions to the questions:

Part 2.2· 3 steps

Your answer: LCM = -25, 960
❌ Incorrect. The LCM cannot be negative.

  1. Find the prime factorization of each number.

    40=23×540 = 2^3 \times 5 120=23×3×5120 = 2^3 \times 3 \times 5 200=23×52200 = 2^3 \times 5^2

  2. Identify the highest power of each prime factor present in any of the factorizations.

    The prime factors are 2, 3, and 5.
    Highest power of 2: 232^3
    Highest power of 3: 313^1
    Highest power of 5: 525^2

  3. Multiply these highest powers together to find the LCM.

    LCM=23×31×52=8×3×25\text{LCM} = 2^3 \times 3^1 \times 5^2 = 8 \times 3 \times 25 LCM=24×25\text{LCM} = 24 \times 25 LCM=600\text{LCM} = 600

    The LCM of 40, 120, and 200 is 600\boxed{600}.

Part 2.3

R160 908.56R 160\,908.56

Your work: "80000-5x15" and "7498923"
❌ Incorrect. This is a compound interest problem, not simple interest or a subtraction.

  1. Identify the principal amount (P), interest rate (r), and number of years (n).

    P=R80 000P = R 80\,000 r=15%=0.15r = 15\% = 0.15 n=5 yearsn = 5 \text{ years}

  2. Use the compound interest formula A=P(1+r)nA = P(1 + r)^n.

    A=80000(1+0.15)5A = 80000(1 + 0.15)^5 A=80000(1.15)5A = 80000(1.15)^5

  3. Calculate the value of (1.15)5(1.15)^5.

    (1.15)5≈2.011357(1.15)^5 \approx 2.011357

  4. Multiply by the principal amount.

    A=80000×2.011357A = 80000 \times 2.011357 A≈160908.56A \approx 160908.56

    Nyeleti will owe approximately R160 908.56\boxed{R 160\,908.56} in 5 years' time.

Part 3

[INTEGERS]

Part 3.19

Your answer: 9

  1. Calculate the powers and the square root.

    23=82^3 = 8 22=42^2 = 4 9=3\sqrt{9} = 3

  2. Substitute these values back into the expression and perform the operations.

    8+4−38 + 4 - 3 12−312 - 3 99

    ✅ Correct. The value is 9\boxed{9}.

Part 3.2-20

Your answer: -26
❌ Incorrect.

  1. Perform the operation inside the parentheses.

    (−8−2)=−10(-8 - 2) = -10

  2. Perform the multiplication.

    3(−7)=−213(-7) = -21

  3. Substitute these values back into the expression and perform the additions/subtractions from left to right.

    11+(−10)+(−21)11 + (-10) + (-21) 11−10−2111 - 10 - 21 1−211 - 21 −20-20

    The value is −20\boxed{-20}.

Part 3.3

27−8\sqrt{27} - 8

Your work: "37−10−64=−3737 - 10 - 64 = -37"
❌ Incorrect. You removed the square root signs.

  1. Calculate the value inside the first square root.

    37−10=27\sqrt{37 - 10} = \sqrt{27}

  2. Calculate the second square root.

    64=8\sqrt{64} = 8

  3. Substitute these values back into the expression.

    27−8\sqrt{27} - 8

    This can also be written as 33−83\sqrt{3} - 8.
    The value is 27−8\boxed{\sqrt{27} - 8} or approximately −2.80\boxed{-2.80}.

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