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.