Question 829757

A number is between 20 and 30 and is three times the sum of its digits.  What is the number?<pre>Let tens and units digits be T and U, respectively
Then number is: 10T + U
So, 20 < 10T + U < 30 ------- inequality (i)
Also, 10T + U = 3(T + U)____10T + U = 3T + 3U___7T = 2U___{{{U = 7T/2}}} ----- inequality (ii)
20 < 10T + {{{7T/2}}}< 30 ------ Substituting {{{7T/2}}} for U in inequality(i) 
40 < 20T + 7T < 60 ----- Multiplying by LCD, 2
40 <    27T   < 60
{{{40/27 < T < 60/27}}} ------ Dividing by 27
{{{1&13/27 < T < 2&6/27}}}

Since tens digit, or {{{T > 1&13/27}}}, but {{{T < 2&6/27}}}, then T or tens digit MUST BE 2
U = 7(2)/2 ------- Substituting 2 for T in inequality (ii)
{{{U = 14/2}}}, or 7

With T being 2 and U being 7, number is: {{{highlight_green(27)}}}
You can do the check!! 

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