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 A real p puzzle (Posted on 2007-10-02)
Determine all possible positive real p satisfying 18[p] + 35{p} = 673, where [y] denotes the greatest integer ≤ y and {y} = y - [y]

 Submitted by K Sengupta Rating: 1.6667 (3 votes) Solution: (Hide) Let [p] = m and {p} = n(say) Then, p=m+n, and: 18m + 35n = 673 Or, n = (673-18m)/35 But 0≤ n< 1 or, 630 < 638< 18m< =673< 684 Or, 35< m< 38 Thus, m = 36, 37 m=36 gives n = 25/35 = 5/7, so that: p = 36 + 5/7 m=37 gives n = 7/35 = 0.2, so that p = 37.2 Thus, p = 36 + 5/7, 37.2---------------------------------------------------- *** Also refer to the solution submitted by Chesca Ciprian in this location, and to the solution submitted by Paul in this location.

 Subject Author Date re: solution slightly differently K Sengupta 2008-03-08 11:38:31 re: Calculus....... K Sengupta 2008-03-08 11:37:46 solution slightly differently Paul 2007-10-04 06:08:22 TWO VALUES FOR P Ady TZIDON 2007-10-02 18:13:36 Calculus....... Chesca Ciprian 2007-10-02 13:35:45

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