The sum of the digits of a two digit number is 6.If 18 is subtracted from the number, the digits in the number are interchanged . Find the number.

unit digit ---- x

tens digit --- y
so the number is 10y + x

10y + x - 18 = 10x + y
9y - 9x = 18
y - x = 2
also: x+y=6
add those last two equation:
2y = 8
y = 4
so x = 2

the number is 42

check:
is 42 - 18 = 24 ? YES

Let's go step-by-step to find the number:

Step 1: Assume the ten's digit of the two-digit number is x.
Step 2: Since the sum of the digits is 6, the units digit would be 6-x.
Step 3: So the original number can be expressed as 10x + (6-x).
Step 4: Simplifying, we get the original number as 9x + 6.

Step 5: We know that when 18 is subtracted from the number, the digits in the number are interchanged.
Step 6: The new number can be written as (6-x)*10 + x.
Step 7: Simplifying, we get the new number as 60 - 9x.

Step 8: Equating the two expressions and solving the equation:
9x + 6 = 60 - 9x
18x = 54
x = 3

Step 9: Now that we have found the value of x as 3, we can substitute it into the original equation from Step 4:
Number = 9x + 6
Number = 9*3 + 6
Number = 27 + 6
Number = 33

Therefore, the two-digit number is 33.

To solve the problem, let's assume that the ten's digit of the two-digit number is x and the unit's digit is y.

From the given information, we know that the sum of the digits is 6.
So we have the equation: x + y = 6.

We are also given that when 18 is subtracted from the number, the digits are interchanged.
This means that the original number can be expressed as 10y + x (since the ten's digit becomes the unit's digit and vice versa).

So we have the equation: (10y + x) - 18 = 10x + y.

Now we have a system of two equations:

x + y = 6 (equation 1)

(10y + x) - 18 = 10x + y (equation 2)

To solve this system of equations, we can use the substitution method.

First, let's solve equation 1 for x:

x = 6 - y.

Now substitute this value of x into equation 2:

(10y + (6 - y)) - 18 = 10(6 - y) + y.

Simplifying this equation:

10y + 6 - y - 18 = 60 - 10y + y

9y - 12 = 60 - 9y

18y = 72

y = 4.

Substitute this value of y back into equation 1 to find x:

x = 6 - y

x = 6 - 4

x = 2.

Therefore, the number is 24.

yes