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Calculate Mr. Bate's electricity bill and Jane's loan interest and total amount.

Mathematics

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3 parts
a

15450 frs\text{15450 frs}

b(i)

30,000 Frs\text{30,000 Frs}

b(ii)

530,000 Frs\text{530,000 Frs}

Step-by-step solution

9 steps

Here are the solutions to the problems:

Part a· 4 steps

Calculate Mr. Bate's electricity bill.

  1. Calculate the cost for the first 100 units.

    The first 100 units are charged at 58.5 frs per unit.

    Cost for first 100 units=100 units×58.5 frs/unit=5850 frs\text{Cost for first 100 units} = 100 \text{ units} \times 58.5 \text{ frs/unit} = 5850 \text{ frs}

  2. Calculate the number of units above 100.

    Mr. Bate consumed a total of 250 units.

    Units above 100=250 units−100 units=150 units\text{Units above 100} = 250 \text{ units} - 100 \text{ units} = 150 \text{ units}

  3. Calculate the cost for the units above 100.

    The units above 100 are charged at 64 frs per unit.

    Cost for units above 100=150 units×64 frs/unit=9600 frs\text{Cost for units above 100} = 150 \text{ units} \times 64 \text{ frs/unit} = 9600 \text{ frs}

  4. Calculate the total bill.

    Total bill=Cost for first 100 units+Cost for units above 100\text{Total bill} = \text{Cost for first 100 units} + \text{Cost for units above 100} Total bill=5850 frs+9600 frs=15450 frs\text{Total bill} = 5850 \text{ frs} + 9600 \text{ frs} = 15450 \text{ frs}

    The total electricity bill for Mr. Bate is 15450 frs\boxed{\text{15450 frs}}.

Part b(i)

30,000 Frs\text{30,000 Frs}

Find the Simple Interest she paid to the bank.

Calculate the simple interest and total amount for Jane's loan.

  1. Identify the given values.

    Principal (P)=500,000 Frs(P) = 500,000 \text{ Frs}
    Rate (R)=2%=2100(R) = 2\% = \frac{2}{100}
    Time (T)=3 years(T) = 3 \text{ years}

  2. Use the Simple Interest formula.

    The formula for Simple Interest (SI) is:

    SI=P×R×T100SI = \frac{P \times R \times T}{100}

  3. Substitute the values and calculate the Simple Interest.

    SI=500,000 Frs×2×3100SI = \frac{500,000 \text{ Frs} \times 2 \times 3}{100} SI=3,000,000100SI = \frac{3,000,000}{100} SI=30,000 FrsSI = 30,000 \text{ Frs}

    The Simple Interest Jane paid is 30,000 Frs\boxed{\text{30,000 Frs}}.

Part b(ii)

530,000 Frs\text{530,000 Frs}

Find the total amount of money she paid back.

  1. Use the formula for Total Amount.

    Total Amount (A)=Principal+Simple Interest(A) = \text{Principal} + \text{Simple Interest}

  2. Substitute the values and calculate the Total Amount.

    A=500,000 Frs+30,000 FrsA = 500,000 \text{ Frs} + 30,000 \text{ Frs} A=530,000 FrsA = 530,000 \text{ Frs}

    The total amount of money Jane paid back is 530,000 Frs\boxed{\text{530,000 Frs}}.

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