Question 137015
let h="hundreds digit", t="tens digit", an u="units digit"


"sum of the digits in a certain three-digit number is 21" __ h+t+u=21


"sum of the first and third digits is twice the middle digit" __ h+u=2t
__ substituting __ t+2t=21 __ t=7
__ substituting __ h+7+u=21 __ h=14-u


" If the hundreds and tens digits are interchanged, the number is reduced by 90" __ 100h+70+u=700+10h+u+90


subtracting 70+u and substituting __ 100(14-u)=700+10(14-u)+20 __ 1400-100u=700+140-10u+20 __ 540=90u __ 6=u


substituting __ h=14-6 __ h=8


876 is the number