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Ade spent 1/2 of his pocket money on food and 1/4 of the remainder on comics. If he had N15 left, how much was the pocket money?

Mathematics

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Answer

D. N40.00\text{D. N40.00}

Step-by-step solution

6 steps
  1. Determine the fraction of money spent on food.

    Let the total pocket money be PP.
    Ade spent 12\frac{1}{2} of his pocket money on food.
    Amount spent on food =12P= \frac{1}{2}P.

  2. Calculate the remainder after buying food.

    The remainder is the total pocket money minus the amount spent on food.
    Remainder =P−12P=12P= P - \frac{1}{2}P = \frac{1}{2}P.

  3. Determine the fraction of money spent on comics.

    Ade spent 14\frac{1}{4} of the remainder on comics.
    Amount spent on comics =14×(12P)=18P= \frac{1}{4} \times (\frac{1}{2}P) = \frac{1}{8}P.

  4. Calculate the fraction of money left.

    The money left is the remainder after food minus the amount spent on comics.
    Money left =12P−18P= \frac{1}{2}P - \frac{1}{8}P.
    To subtract these fractions, find a common denominator, which is 8.

    48P−18P=38P\frac{4}{8}P - \frac{1}{8}P = \frac{3}{8}P
  5. Solve for the total pocket money.

    We are given that Ade had N15 left.
    So, we set the fraction of money left equal to N15:

    38P=15\frac{3}{8}P = 15

    To find PP, multiply both sides by 83\frac{8}{3}:

    P=15×83P = 15 \times \frac{8}{3} P=15×83P = \frac{15 \times 8}{3} P=5×8P = 5 \times 8 P=40P = 40

    The total pocket money was N40.00.

  6. Compare the result with the given options.

    The calculated pocket money is N40.00, which corresponds to option D.

    The final answer is D. N40.00\text{D. N40.00}.

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