The sum of the digits of a two-digit number is 5. If 9 is subtracted from the number, the digits will be interchanged. Find the number.
it is 32
what is the equation?
To solve this problem, we need to set up equations based on the given information.
Let's assume the tens digit of the two-digit number is x, and the units digit is y.
According to the problem, the sum of the digits is 5, so we can write the equation: x + y = 5.
Also, if we subtract 9 from the number, the digits will be interchanged. This means that the new number can be written as 10y + x. So, the equation becomes: 10y + x = 10x + y - 9.
Now we have a system of equations:
x + y = 5
10y + x = 10x + y - 9
To solve this system, we can use the substitution method or elimination method. Let's use the substitution method:
From the first equation, we can solve for x in terms of y:
x = 5 - y
Substituting this into the second equation, we get:
10y + (5 - y) = 10(5 - y) + y - 9
10y + 5 - y = 50 - 10y + y - 9
9y + 5 = 50 - 9y - 9
9y + 5 = 41 - 9y
Now, let's simplify the equation:
18y = 36
y = 2
Substituting y = 2 into the first equation:
x + 2 = 5
x = 3
Therefore, the two-digit number is 32.
What is your answer?
We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.