Q. An Eraser, Pencil, Notebook together costs $1.00. Notebook costs more than the cost of 2 Pencils. 3 Pencil costs more than 4 Erasers. 3 Erasers costs more than a Notebook. How much does a pencil costs?

• Given:
  P + E + N = 100 cents
  
  N > 2 P
  3 P > 4 E
  3 E > N
  
  3 P > 4 E → 2 P > 8/3 E
  N > 2 P → N > 8/3 E
  N < 3 E (given)
  Therefore: 8/3 E < N < 3 E
  
  3P > 4 E → P > 4/3 E
  2P < N → P < N/2
  N < 3 E → N/2 < 3/2 E
  Therefore: 4/3 E < P < 3/2 E
  
  Converting those to sixths, we have
  16/6 E < N < 18/6 E or N = roughly 17 / 6 E
  8/6 E < P < 9/6 E or P = roughly 8.5 / 6 E
  
  Now try some values for E:
  E P N Total
  6 8.5 17 31.5
  12 17 34 63
  18 25.5 51 94.5
  That's close to 100, so with a bit of fiddling, we can make it:
  E = 19 P = 26 N = 55 Total = 100
  
  Checking the conditions:
  N > 2 P ? ... 55 > 2 * 26 ? ... .. 55 > 52 ... yes
  3 P > 4 E ? . 3 * 26 > 4 * 19 ? . 78 > 76 .. yes
  3 E > N ? ... 3 * 19 > 55 ? ... .. 57 > 55 ... yes
  
  Answer:
  Eraser: 19 cents
  Pencil: 26 cents
  Notebook: 55 cents
• 9 years agoHelpfull: Yes(0) No(0)