the sum of the digits of a two-digit number is 7. when digits are reversed, the number is increased by 27. algebraically, find the original 2-digit # ?

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the sum of the digits of a two-digit number is 7. when digits are reversed, the number is increased by 27. algebraically, find the original 2-digit # ?

Posted 268 day ago

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Answers (6)

since reversing digits increases their sum, so the second digit must be larger. Then, possible digits will be: 34, 25 and 16. Reversing these pairs will give: 43, 52, and 61. It is seen immediately that
43-34=9
52-25=27, and
61-16=45.
so the original 2digt number is 25.

Posted 230 day ago

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Amar Soni

Because the number is of two digit, let x is at tenth place and y is at unit place.
Now x+y=7 given....................................................(i)
The number will be 10x+y.....................................(ii)
When the digits are interchanged then number willbe=10y+x......................(iii)
As per given condition
{10y+x}-{10x+y}=27...............................................................(iv)
9y-9x=27, by dividing by 9 we get
y-x=3...............................................(v)
Solve (i) and (v), we get
x=2 and y=5
The orginal number was 25 and by reversing digits new number will be 52
The difference between 52 and 25 is 27

Posted 250 day ago

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tutorsTeach

3+4, 34 ---> it was just an example, jdrew39.

Posted 262 day ago

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mjoelg

25

Posted 263 day ago

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jdrew39

The sum of 3+4 is 7. 27+7=34

Posted 264 day ago

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tutorsTeach

Let the 2-digit number be 10x+y (e.g., 35 would be 10x3 + 5)
Then, the "digits" are 10x and y
Let the sum of those 'digits' be x+y equal 7: x+y=7 (e.g., in the number 34 that sum would be 3+4=7)
Now, the "opposite" of our number 10x+y would be 10y+x (e.g., 43 would be 10x4+3)
Now, the oposite number would increase our number (10x+y) by 27, so we have an algebraic equation:
10y+x = 10x+y+27
The other equation we need to solve these two variables is:
x+y=7, because the sum of x and y (or 4 and 3 for instance) will be 7
So, the pair of equations is:
10y+x = 10x+y+27
y+x = 7
As you solve this pair of eqation, you get:
y=5 and x=2
To test it, we will display:
25 and 52. 52 is larger than 25 by 27 exactly.

Posted 268 day ago

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