A 2 digit number is increased by 36 when the digits are reversed. The sum of the digits is 10. Find the original number.
If the number is xy (digits are x and y), then
10y+x = 10x+y + 36
x+y = 10
Now just find x and y
Let's assume the original 2-digit number is represented by ab, where a is the tens digit and b is the units digit.
According to the problem, when the digits are reversed, we get a new number ba. The difference between the new number and the original number is 36, so we can write this as an equation:
10b + a - (10a + b) = 36
Simplifying the equation gives:
10b + a - 10a - b = 36
9b - 9a = 36
Dividing both sides of the equation by 9, we get:
b - a = 4
Since the sum of the digits is 10, we know that a + b = 10. Solving this system of equations will give us the values of a and b.
b - a = 4
a + b = 10
To solve this system of equations, we can add the two equations together:
(b - a) + (a + b) = 4 + 10
2b = 14
Dividing both sides of the equation by 2 gives:
b = 7
Now we can substitute the value of b into the equation a + b = 10:
a + 7 = 10
Subtracting 7 from both sides of the equation gives:
a = 3
Therefore, the original number is 37.
To solve this problem, we need to find a two-digit number that increases by 36 when its digits are reversed. We are also given that the sum of the digits is 10.
Let's assume the original number is written as "AB" (where A is the tens digit and B is the ones digit). When the digits are reversed, the new number becomes "BA".
According to the problem, the new number (BA) is 36 greater than the original number (AB). Mathematically, we can express this as:
10B + A + 36 = 10A + B
This equation represents the value of BA (10B + A) being 36 greater than the value of AB (10A + B).
Now, let's simplify the equation:
10B + A + 36 = 10A + B
9B - 9A = 36
B - A = 4 (dividing both sides by 9)
Since the original number is a two-digit number and the sum of its digits is 10, we know that A + B = 10.
Now, we have a system of two equations:
B - A = 4
A + B = 10
We can solve this system of equations to find the values of A and B.
By adding the two equations together, we get:
(A + B) + (B - A) = 10 + 4
2B = 14
B = 7
Substituting B = 7 back into A + B = 10, we find:
A + 7 = 10
A = 3
So the original number is 37.