The sum of the digits of a two-digit number is 11. If the digits are reversed, the number is increased by 45. Find the original number
2 + 9
3 + 8
4 + 7
5 + 6
Which of those pairs is it?
3+8
Right.
To solve this problem, we need to set up equations based on the given information. Let's call the tens digit of the original number "x" and the units digit "y".
According to the problem, the sum of the digits is 11. Therefore, the equation is:
x + y = 11 ----(Equation 1)
It is also given that if the digits are reversed, the number is increased by 45. This means that the reversed number is equal to the original number plus 45. Since the original number is a two-digit number, we can say that:
10y + x = 10x + y + 45 ----(Equation 2)
To solve this system of equations, we will use the method of elimination.
First, let's rewrite Equation 2 by rearranging the terms:
10y - y = 10x - x + 45
9y = 9x + 45
Next, divide both sides of the equation by 9 to simplify:
y = x + 5 ----(Equation 3)
Now, substitute Equation 3 into Equation 1:
x + (x + 5) = 11
2x + 5 = 11
Subtract 5 from both sides:
2x = 6
Divide both sides by 2:
x = 3
Now that we have found the value of x, we can substitute it back into Equation 1 to find y:
3 + y = 11
y = 11 - 3
y = 8
Therefore, the original number is 38.