The sum of the digits in a two digit number is 7. If we add 9 to the number, the digits are interchanged. Find the number.
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The sum of the digits in a two digit number is 7. If we add 9 to the number, the digits are interchanged. Find the number.
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Step-by-step explanation:
Let a be the first digit and b be the second digit. The two digit number ( which looks like ab ) value is 10a+b
Also it is given that a+b=7 -- ( 1 )
When the digits are interchanged ( it looks like ba ) the number's value becomes 10b+a
It is given that adding 9 to the original number makes it 10b+a ( interchanged )
So, 10a+b+9=10b+a
Moving "a" and "b" terms to left side and moving numericals to right side,
10a+b−10b−a=−9
9a−9b=−9
9(a−b)=−9
a−b=−1
a=b−1
Substituting for a in ( 1 ), we get,
b−1+b=7
2b=7+1=8
b=82=4
Hence a=b−1=4−1=3
Hence original number is 34 and new number is 43.
Answer:
The number is 34
Step-by-step explanation:
x + y = 7 ...(1)
10x + y + 9 = 10y + x
9x + 9 = 9y
x + 1 = y ...(2)
Substituting (2) in (1):
x + (x + 1) = 17
2x = 6
x = 3
Therefore, y = 3