Question 1041233
I shall write a two digit number sum of two digit number is 14 and if 29 is subtracted from the number two digits will be equal .Led us from the simultaneous equations by solving them let us see what will be the two digit number.
<pre>Let original number’s tens and units digits be T and U, respectively
Let new number’s tens and units digit be {{{T[S]}}}
Then: T + U = 14_____T = 14 - U ------ eq (i)
Also, {{{10T + U - 29 = 10T[S] + T[S]}}}_____{{{10T + U - 29 = 11T[S]}}} ------ eq (ii)
{{{10(14 - U) + U - 29 = 11T[S]}}} ------ Substituting 14 - U for T in eq (ii)
{{{140 - 10U + U - 29 = 11T[S]}}}
{{{111 - 9U = 11T[S]}}}
{{{11T[S] + 9U = 111}}}
{{{9U = 111 - 11T[S]}}}  
{{{U = (111 - 11T[S])/9}}}
{{{T[S]}}} CANNOT be small digits since that’d make U, or the units digit a 2-digit number, so we start {{{T[S]}}} with the largest digits. 

Substituting 9, 8, and 7 for {{{T[S]}}} into the equation: {{{U = (111 - 11T[S])/9}}}DOES NOT produce an INTEGER for U that's a multiple of 9. However, 6 did. 

{{{U = (111 - 11T[S])/9}}}
{{{U = (111 - 11 * 6)/9}}} ------ Substituting {{{matrix(1,3, 6, for, T[S])}}}
{{{U = (111 - 66)/9}}}
U = {{{45/9}}}, or 5 

T = 14 - 5 -------- Substituting 5 for U in eq (i)
T, or tens digit = 9

Original number: {{{highlight_green(95)}}}</pre>