求教数学题谢谢

taohuaxianzi

求教数学题谢谢

　AＢ

+ BA

AAC

In the correctly worked addition problem shown, where

the sum of the two-digit positive integers AB and BA is

the three-digit integer AAC, and A, B, and C are different digits, what is the units digit of the integer AAC?

A. 9

B. 6

C. 3

D. 2

E. 0

这道题如果不代数字算应该怎么个思路呢？?/谢谢

taohuaxianzi

I  see,  thanks  a  lot !!!!

luoye1

设AB=10a＋b

则BA＝10b＋a，AAC＝100a＋10a＋c

10a＋b＋10b＋a=100a+10a+c

推出11b－99a＝c a、b、c都》＝0

则b＝9，a＝1，c＝0