Mechanical Pencils

Algebra Level pending

I only buy mechanical pencils at the beginning of the school year. The school year is 36 weeks long. If I lose one pencil every 2 weeks (to include the first and last weeks of the school year), but find one every 3 weeks, how many should I buy so that I finish the year with 5 pencils?


The answer is 11.

Sarah Preston by Sarah Preston , 20, USA

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1 solution

Arthur Hertz
Oct 9, 2016

Assume x is the initial number of pencils, and P(w) is pencils as a function of weeks, and P(36) = 5:

  • P(w) = x - w 2 \frac{w}{2} + w 3 \frac{w}{3} = x - w 6 \frac{w}{6} .
  • P(36) = x - 36 6 \frac{36}{6} = x - 6 = 5. Substitute 36 for w.
  • x = 11. Solve for x.
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