The sum of the two digits of a number is 11 .the difference between the original number and the number formed by interchanging the digits is 9 .find the number.
How about you showing me some of your steps, now that I have done two very similar to this one for you ?
To find the number, we need to set up some equations based on the given information.
Let's assume the original number is a two-digit number, with digits x and y. According to the problem, the sum of the two digits is 11:
x + y = 11 ----- equation (1)
It is also mentioned that the difference between the original number and the number formed by interchanging the digits is 9. To find this difference, we subtract the number formed by interchanging the digits from the original number:
(10x + y) - (10y + x) = 9
Simplifying this equation will give us:
9x - 9y = 9
x - y = 1 ----- equation (2)
Now we have two equations with two variables, which we can solve simultaneously.
To solve the system of equations (1) and (2), we can use the method of substitution or elimination.
Using substitution, we can express x in terms of y from equation (2):
x = y + 1
Substituting this value of x into equation (1):
(y + 1) + y = 11
2y + 1 = 11
2y = 10
y = 5
Now that we have the value of y, we can substitute it back into equation (2) to find x:
x - 5 = 1
x = 6
Therefore, the original number is 65.
So, the answer is 65.