A number of two digits is increased by 9. When the digits are reversed, the sum of the digits is 5. Find the number.

let's work backwards,

by looking at the number after it was reversed.
Since the sum of the digits is 5
it could only be
14, 41, 23, or 32
but that result is caused by having added a 9
so the original number could only be:

9 , not a two digit number, so NO
32
14
23

So the number could have been 32, 14, or 23

check:
32+9 = 41, sum of digits is 5
14+9 = 23, sum of digits is 5
23+9 = 32, sum of digits is 5

Let's assume the number is represented as "10x + y", where x and y are the tens and ones digits, respectively.

According to the problem statement, when we increase the number by 9, we get "10x + y + 9". Reversing the digits gives us "10y + x".

The problem also states that the sum of the digits when reversed is 5. This can be written as:

x + y = 5

Now, we can write the equation using the given information:

10x + y + 9 = 10y + x

Simplifying the equation, we get:

9x - 9y = -9

To solve for x and y, we can divide the equation by 9:

x - y = -1

Now, we have a system of linear equations:

x + y = 5
x - y = -1

We can solve this system using the method of elimination.

Adding both equations, we eliminate the variable 'y':

2x = 4

Dividing by 2, we find:

x = 2

Substituting the value of 'x' into either equation, we can find 'y':

2 + y = 5
y = 3

Therefore, the number is 23.

To solve this problem, let's represent the number of two digits as 10x + y, where x represents the tens digit and y represents the ones digit. Given that the number is increased by 9, we can create the equation:

10x + y + 9

After reversing the digits, we get a new number represented by 10y + x. The sum of the digits is 5, so we have the equation:

x + y = 5

Now, we can set up a system of equations using the given information:

10x + y + 9 = 10y + x
x + y = 5

Simplifying the first equation, we have:

10x + y + 9 = 10y + x
9x - 9y = -9

Now we can solve the system of equations. We can use the method of substitution by rearranging the second equation to solve for x:

x = 5 - y

Substituting this into the first equation:

9(5 - y) - 9y = -9
45 - 9y - 9y = -9
-18y = -54
y = 3

Now substitute the value of y back into the second equation to solve for x:

x + 3 = 5
x = 2

Therefore, the number is 10x + y = 10(2) + 3 = 20 + 3 = 23.

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