SOLUTION: 1 A + A ___________ _____ 2 B in the correctly solved addition problem above, A and B represent di

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Question 296012: 1 A
+ A
_________________
2 B
in the correctly solved addition problem above, A and B represent digits . if A is not equal to B ,how many different digits from 0 through 9 could A represent ?
(A) two (B) three (C) five (D) seven (E) nine

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

The number "1A" is 10%2BA
The number "2B" is 20%2BB

So since 

"1A" + A = "2B",

%2810%2BA%29%2BA=20%2BB
10%2BA%2BA=20%2BB
10%2B2A=20%2BB
2A=10%2BB
B=2A-10
B=2%28A-5%29
0%3C=B%3C=9
0%3C=2%28A-5%29%3C=9
0%3C=2A-10%3C=9
Add 10 to all three sides:
10%3C2A%3C=19
5%3C=A%3C=9.5
5%3C=A%3C=9

So the different digits from 0 through 9 which A could represent are 
the five numbers 5,6,7,8,9 

So the answer if five.

If A=5, then B=2A-10 = 2(5)-10 = 10-10 = 0

15
+5
--
20

If A=6, then B=2A-10 = 2(6)-10 = 12-10 = 2

16
+6
--
22

If A=7, then B=2A-10 = 2(7)-10 = 14-10 = 4

17
+7
--
24

If A=8, then B=2A-10 = 2(8)-10 = 16-10 = 6

18
+8
--
26

If A=9, then B=2A-10 = 2(9)-10 = 18-10 = 8

19
+9
--
28

Edwin