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The sum of the digits of a 2-digit number is 11. If the digits are reversed, the number formed is 45 more than the original number. Find the original number. If x is the ten's digit and y is the one's digit, the original number is 10x+y. the number with reversed digits is 10y+x.

User Rowhawn
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Answer:shoo ion kno

Step-by-step explanation:

User Ponder Stibbons
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The original number is 38

Step-by-step explanation:

Let the sum of the digits of a 2 digit number is 11.

If the digits are reversed, the number formed is 45 more than the original number.

Let x and y be the two numbers and
x+y=11

Let the original number be
10x+y

Let the reversed number be
10y+8

We need to determine the original number.

Original number:

We need to determine the original number
10x+y

Thus, we have,


x+y=11 -----(1)


(10x+y)+45=10y+x --------(2)

Solving the equation (2), we get,


10x+y+45-10y-x=0


9x-9y=-45


9(x-y)=-45


x-y=-5 --------(3)

Adding the equations (1) and (3), we get,


2x=6


x=3

Thus, the value of x is 3

Substituting
x=3 in equation (1), we get,


3+y=11


y=8

Thus, the value of y is 8.

The equation of the original number is
10x+y

Substituting the value of x and y, we get,

Original number =
10(3)+8\implies 30+8=38

Thus, the original number is 38.

User Denis Tsoi
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