Question 150546
Let t=tens digit and u=units digit


So the unknown number is {{{n=10t+u}}}



Since "Twice the tens digit of a number is the same as the units digit", this means that {{{2t=u}}} (or {{{u=2t}}}). Also, because the "number is 6 greater than 5 times the units digit", this means that {{{n=5u+6}}}



{{{n=5u+6}}} Start with the second equation.



{{{10t+u=5u+6}}} Plug in {{{n=10t+u}}}



{{{10t+2t=5(2t)+6}}} Plug in {{{u=2t}}}



{{{10t+2t=10t+6}}} Multiply.



{{{12t=10t+6}}} Combine like terms on the left side.



{{{12t-10t=6}}} Subtract {{{10t}}} from both sides.



{{{2t=6}}} Combine like terms on the left side.



{{{t=(6)/(2)}}} Divide both sides by {{{2}}} to isolate {{{t}}}.



{{{t=3}}} Reduce.



So the tens digit is {{{t=3}}}. 



{{{u=2t}}} Go back to the first equation



{{{u=2(3)}}} Plug in {{{t=3}}}



{{{u=6}}} Multiply



So the units digit is {{{u=6}}}. This means that the number is {{{n=36}}}