Respuesta :
The original number is 38
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 [tex]x+y=11[/tex]
Let the original number be [tex]10x+y[/tex]
Let the reversed number be [tex]10y+8[/tex]
We need to determine the original number.
Original number:
We need to determine the original number [tex]10x+y[/tex]
Thus, we have,
[tex]x+y=11[/tex] -----(1)
[tex](10x+y)+45=10y+x[/tex] --------(2)
Solving the equation (2), we get,
[tex]10x+y+45-10y-x=0[/tex]
[tex]9x-9y=-45[/tex]
[tex]9(x-y)=-45[/tex]
[tex]x-y=-5[/tex] --------(3)
Adding the equations (1) and (3), we get,
[tex]2x=6[/tex]
[tex]x=3[/tex]
Thus, the value of x is 3
Substituting [tex]x=3[/tex] in equation (1), we get,
[tex]3+y=11[/tex]
[tex]y=8[/tex]
Thus, the value of y is 8.
The equation of the original number is [tex]10x+y[/tex]
Substituting the value of x and y, we get,
Original number = [tex]10(3)+8\implies 30+8=38[/tex]
Thus, the original number is 38.
