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A real p puzzle (Posted on 20071002) 

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:

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Let [p] = m and {p} = n(say)
Then, p=m+n, and:
18m + 35n = 673
Or, n = (67318m)/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.

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