Question 551145
wow im dizzy just reading this
two digit number will be: {{{ab}}} and ab={{{10a+b}}} ex:10(1)+2=12
so {{{10a+b=2+3b}}}
interchanged means {{{ba}}} which is {{{10b+a}}}
so {{{10b+a=4(10a+b)-24}}}
now we have 2 equations solve  one equation for 1 variable then use substitution in other equation
{{{10a+b=2+3b}}}
{{{10a=2+2b}}}
{{{a=(1+b)/5}}}
.
{{{10b+a=4(10a+b)-24}}}simplify
{{{10b+a=40a+4b-24}}}
{{{6b=39a-24}}} substitute a
{{{6b=39((1+b)/5)-24}}}distribute 39
{{{6b=((39+39b)/5)-24}}} multiply all by 5
{{{30b=39+39b-120}}} add like terms
{{{30b=39b-81}}}add 81 and subtract 30b
{{{81=9b}}}divide
{{{9=b}}}
.
{{{a=(1+b)/5}}}
{{{a=(1+9)/5}}}
{{{a=10/5}}}
{{{a=2}}}
.
your number is {{{highlight(29)}}}
and interchanged is 92 lets check
{{{10a+b=2+3b}}}
{{{29=2+3(9)}}}
{{{27=3(9)}}}
{{{27=27}}}
correct
{{{10b+a=4(10a+b)-24}}}
{{{92=4(29)-24}}}
{{{92=(116)-24}}}
{{{92=92}}}
correct


that was fun got another one? Have a Happy New Year