Question 1043164
{{{x}}}= the larger digit
{{{y}}}= the smaller digit
"Three times the larger digit exceeds three times the smaller by three" translates as
{{{3x=3y+3}}}<-->{{{3*x=3(y+1)}}}<-->{{{x=y+1}}} .
That narrows the possibilities to
10, 12, 21, 23, 32, 34, 43, 45, 54, 56, 65, 67, 76, 78, 87, 89, and 98.
What other clue do we have?

{{{t}}}= the tens digit
{{{u}}}= the ones digit
{{{t+u}}}= the sum of the digits
{{{10t+u}}}= the value of the number
The "number of two digits is equal to five times the sum of the digits"
translates into the equation
{{{10t+u=5(t+u)}}}<-->{{{10t+u=5t+5u}}}<-->{{{10t-5t=5u-u}}}<-->{{{5t=4u}}}<-->{{{t=(4/5)*u}}} .
Maybe by now you realize that the number is {{{highlight(45)}}}.
Otherwise, {{{t=(4/5)*u}}} tells you that {{{t}}} is the smaller digit, so {{{u=t+1}}} .
{{{system(u=t+1,5t=4u)}}}--->{{{system(u=t+1,5t=4(t+1))}}}--->{{{system(u=t+1,5t=4t+4)}}}--->{{{system(u=t+1,5t-4t=4)}}}--->{{{system(u=t+1,t=4)}}}--->{{{system(u=4+1,t=4)}}}--->{{{highlight(system(u=5,t=4))}}}