Question 994025
Reversing the digits of a three-digit number, the hundreds digit and the units digit exchange places.
So, if after reversing the digits, the new number is the same as the original number,
the hundreds digit must be the same as the units digit.
{{{x}}}= hundreds digit = units digit
{{{y}}}= tens digit
{{{x+y+x=2x+y}}}= sum of the digits
"The sum of the digits of a three-digit number is 18" translates as
{{{2x+y=18}}} .
"The units digit is one less than twice the tens digit" translates as
{{{x=2y-1}}} .
{{{system(x=2y-1,2x+y=18)}}}--->{{{system(x=2y-1,2(2y-1)+y=18)}}}--->{{{system(x=2y-1,4y-2+y=18)}}}--->{{{system(x=2y-1,5y-2=18)}}}--->{{{system(x=2y-1,5y=18+2)}}}--->{{{system(x=2y-1,5y=20)}}}--->{{{system(x=2y-1,y=20/5)}}}--->{{{system(x=2y-1,y=4)}}}--->{{{system(x=2*4-1,y=4)}}}--->{{{highlight(system(x=7,y=4))}}} .
So the number is {{{highlight(747)}}} .