Eva is adding two 4-digit numbers together. The answer has a five in the tens column where an exchange has taken place. What digits could be in the tens column of the two numbers being added together?
Please help my little brother.
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Given:
Two 4-digit numbers which are added together.
The answer has a five in the tens column where an exchange has taken place.
To Find:
The digits that could be in the tens column of the two numbers being added together.
Solution:
- We have to deal with the tenth place in 4 digit number.
- Number at units place can have a maximum value of 9.
- Therefore, 9 + 9 = 18.
- Therefore, at the worst case it can have a carry of 1.
- Therefore carry can be either 0 or 1 at Tenth's place.
- Now Number at tenth's place of the sum is 5.
- Therefore possible numbers at tenth's place of the numbers being added are:
- Carry = 0 : (1 , 4 ) , ( 0, 5 ) , (6, 9 ) , ( 7 , 8 )
- Carry = 1 : (1 , 3 ) , ( 2 , 2 ) , (0, 4 ) , ( 9 , 5 ) , ( 6 , 8 ) , ( 7, 7 ).
Digits could be in the tens column of the two numbers being added together? are (1 , 4 ) , ( 0, 5 ) , (6, 9 ) , ( 7 , 8 ) if carry is 0 and (1 , 3 ) , ( 2 , 2 ) , (0, 4 ) , ( 9 , 5 ) , ( 6 , 8 ) , ( 7, 7 ) if carry is 1.
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