Question 1067202
t,h,u, for tens hundreds ones


{{{100h+10t+u}}}, the number


{{{system(100h+10t+u=17(h+t+u),100h+10t+u+198=h+10t+100u,h+u=t-1)}}}


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{{{100h+10t+u-17h-17t-17u=0}}}
{{{83h-7t-16u=0}}}
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{{{100h+10t+u-h-10t-100u+198=0}}}
{{{99h-99u=-198}}}
{{{h-u=-2}}}
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{{{h+u-t=-1}}}



Revised system of equations: {{{system(83h-7t-16u=0,h-u=-2,h+u-t=-1)}}}


Substitute using t=h+u+1 into the first equation.
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{{{83h-7(h+u+1)-16u=0}}}
{{{83h-7h-7u-7-16u=0}}}
{{{76h-23u=7}}}
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Simpler system in two variables,  {{{system(76h-23u=7,u-h=2)}}}


{{{76h-23u+(23u-23h)=7+46}}}
{{{76h-23h=53}}}
{{{53h=53}}}
{{{highlight(h=1)}}}-------the Hundreds place



Again using the simpler system
{{{u-h=2}}}
{{{u=2+h}}}
{{{u=2+1}}}
{{{highlight(u=3)}}}--------the Ones place



Returning to the Revised System equation of t=h+u+1
{{{t=1+3+1}}}
{{{highlight(t=5)}}}



The three digit number is  153.