perplexus.info :: Just Math : A real p puzzle

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: 2.5000 (4 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

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*** Also refer to the solution submitted by Chesca Ciprian in this location, and to the solution submitted by Paul in this location.

Comments: ( You must be logged in to post comments.)

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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