Question 630292: AB + BA= 1A4
in the correctly worked addition problem above, A and B represent two different digits. what digit does A represent?
*please include explanations
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! The value of AB is 10A + B, while the value of BA is 10B + A.
In the equation, AB + BA = 1A4, substitute the values of AB and BA above:
(10A + B) + (10B + A) = 100 + 10A + 4
Subtract 10A from each side:
B+ 10B + A = 104
11B + A = 104
Subtract A from each side:
11B = 104 - A
Since B must be an integer, this means that you must subtract an integer value of A from 104 and obtain a multiple of 11.
If A = 1, you have 11B=103. 103 is not a multiple of 11.
If A = 2, you have 11B=102.
If A = 3, you have 11B=101.
If A = 4, you have 11B=100.
If A = 5, you have 11B=99, so B = 9. It works!!
Check: AB= 59, BA= 95,
AB + BA = 1A4
59 + 95 = 154, so it checks!!
Congratulations on a NICE PROBLEM!! I liked this one VERY MUCH!!
For additional help with this topic and other algebra topics, please see my own FREE website at www.mathinlivingcolor.com.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
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