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Nolan has 4 times as many pens as Fiona, and Fiona has 6 times as many pencils as Nolan. If Nolan has a total of 23 pens and pencils, and so does Fiona, which of these is a number of pens or a number of pencils that either Nolan or Fiona has?

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francocanacari

Nolan has 20 pens and 3 pencils, while Fiona has 5 pens and 18 pencils.

Amount determination

Given that Nolan has 4 times as many pens as Fiona, and Fiona has 6 times as many pencils as Nolan, to determine, if Nolan has a total of 23 pens and pencils, and so does Fiona, the number of pens and pencils that either Nolan or Fiona has, the following calculation must be performed:

  • Pen = A
  • Pencil = B
  • N = 14A + 9B = 23 /// F = 3.5 + 19.5
  • N = 12A + 11B = 23 /// F = 3A + 20B
  • N = 20 A + 3 B = 23 /// F = 5 A + 18 B
  • 20 / 4 = 5
  • 18 / 6 = 3

Therefore, Nolan has 20 pens and 3 pencils, while Fiona has 5 pens and 18 pencils.

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