If a,b,c represents digits from 1 to 9 such that 1ab+cca=697 and there is no carry - over in addition , find the value of a+b+c.
Answers
Given data :
a,b,c represents digits from 1 to 9 such that 1ab+cca=697 and there is no carry - over in addition
To find : The value of a+b+c
Step by step solution :
As per the given data, 1ab + cca = 697 can be written in the format of :
1 a b
+ c c a
----------------
6 9 7
----------------
KEY POINT : No carry over addition.
So, we can simply form the equations as :
b + a = 7 ------------- eq(1)
a + c = 9 ------------- eq(2)
1 + c = 6 ------------- eq(3)
Solving eqn 3, we get
1 + c = 6
⇒ c = 6 - 1
⇒ c = 5
As we get the value of c as 5, substitute it in the eqn 2 to get the value of a, as in :
a + c = 9
⇒ a + 5 = 9
⇒ a = 9 - 5
⇒ a = 4
Now, substitute this 'a' value in the eqn 1 to get the value of 'b' :
b + a = 7
⇒ b + 4 = 7
⇒ b = 7 - 4
⇒ b = 3
Hence, we got the values of a, b, c as 4, 3, 5 respectively.
Then, a + b + c = 4 + 3 + 5 = 12
Therefore, the value of a + b + c = 12.
Check :
1ab = 143 , cca = 554
1ab + cca = 143 + 554 = 697 = given answer
Hence, it is proved that the values of a, b, c resulted out are correct.
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Answer:
1+C=6
C=5
A+C=9⇒A=4
Now, B+A=7
Hence A+B+C=12
