The sum of the digits of a two-digit number is 13. If the digits are reversed, the new number is 9 more than the original number. Find the original number
What have you found?
To find the original number, we need to set up a system of equations based on the given information.
Let's call the tens digit of the original number "x" and the ones digit "y".
From the statement "the sum of the digits is 13," we can write the equation:
x + y = 13
From the statement "if the digits are reversed, the new number is 9 more than the original number," we can write the equation:
10y + x = 10x + y + 9
To solve this system of equations, we can use the method of substitution.
First, let's solve the first equation for x:
x = 13 - y
Now substitute this value for x in the second equation:
10y + 13 - y = 10(13 - y) + y + 9
Simplifying the equation:
10y + 13 - y = 130 - 10y + y + 9
Combining like terms:
9y + 13 = 139 - 9y
Moving all the variables to one side:
9y + 9y = 139 - 13
Combining like terms:
18y = 126
Dividing both sides by 18:
y = 7
Now substitute this value for y back into the first equation to solve for x:
x + 7 = 13
Subtracting 7 from both sides:
x = 6
Therefore, the original number is 67.