Question 153381
What is a two digit number equal to three times the product of its digits?
<pre><font size = 4 color = "indigo"><b>
{{{10t + u = 3tu}}}

Solve for u

{{{10t=3tu-u}}}

{{{10t=u(3t-1)}}}

{{{10t/(3t-1)=u}}}

Do long division using only integers:

    <u>     3</u> 
3t-1)10t+0
      <u>9t-3</u>
       t+3

{{{3+(t+3)/(3t-1)=u}}}

So we can tell from that that

u must be larger than 3.  So try u = 4

{{{10t + u = 3tu}}}

{{{10t + (4) = 3t(4)}}}

{{{10t + 4 = 12t}}}

{{{4=2t}}}

{{{2=t}}}

So 24 is a solution

The product of its digits is 8, and 24 is 3 times 8.

Try u=5

{{{10t + u = 3tu}}}

{{{10t + (5) = 3t(5)}}}

{{{10t + 5 = 15t}}}

{{{5=5t}}}

{{{1=t}}} 

So 15 is another solution

The product of its digits is 5, and 15 is 3 times 5.

Those are the only two solutions.

Edwin</pre>