SOLUTION: C 9 7 3 + 6 B ________ A A 3 A, B, and C are digits in the correctly solved problem above. Which of the following is equal to A-B+C? a) 9 b) 10 c) 11 d) 12 e

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: C 9 7 3 + 6 B ________ A A 3 A, B, and C are digits in the correctly solved problem above. Which of the following is equal to A-B+C? a) 9 b) 10 c) 11 d) 12 e      Log On


   

Question 882838: C 9
7 3
+ 6 B
________
A A 3
A, B, and C are digits in the correctly solved problem above. Which of the following is equal to A-B+C?
a) 9
b) 10
c) 11
d) 12
e)13
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Looking at the ones digits:
0%3C=B%3C=9
9%2B3%2B0%3C=9%2B3%2BB%3C=9%2B3%2B9
12%3C=9%2B3%2BB%3C=21
Since the ones digit of 9%2B3%2BB is 3 ,
9%2B3%2BB=13-->12%2BB=13-->B=13-12-->highlight%28B=1%29
When adding the tens digits, we have the 1 ten from 9%2B3%2BB=13 carried over.
1%2BC%2B7%2B6=10A%2BA
C%2B14=%2810%2B1%29A
C%2B14=11A
So C%2B14 is the multiple of 11 11A .
Since 0%3C=C%3C=9 ,
0%2B14%3C=C%2B14%3C=9%2B14
14%3C=C%2B14%3C=23
The only C%2B14=11A multiple of 11 between 14 and 23 is
11%2A2=22 .
So 11A=11%2A2--->highlight%28A=2%29 and
C%2B14=22--->C=22-14--->highlight%28C=8%29 .
Then, A-B%2BC=2-1%2B8--->highlight%28A-B%2BC=9%29 .