Question 892614
<pre>
tens digit = t
ones digit = u
number = 10t+u

the ones digit multiplied by five and the 
tens digit by three and the result added = 5u+3t
</pre>
her total is the same as the integer she chose
<pre>
{{{5u+3t}}}{{{""=""}}}{{{10t+u}}}
   {{{4u}}}{{{""=""}}}{{{7t}}}

Divide both sides by 4t

   {{{4u/(4t)}}}{{{""=""}}}{{{7t/(4t)}}}

 {{{cross(4)u/(cross(4)t)}}}{{{""=""}}}{{{7cross(t)/(4cross(t))}}}

    {{{u/t}}}{{{""=""}}}{{{7/4}}}

The only digits in the ratio u:t = 7:4 are u=7 and t=4.

So the number is 47.

Checking:  5×7+3×4 = 35+12 = 47

Edwin</pre>