A number consist of two digits whose sum is 9, if 27 is subtracted from the number the digits are reversed. Find the number. 

Let's denote the two-digit number as \( \text{AB} \), where \( A \) is the tens digit and \( B \) is the units digit.

Given:
1. The sum of the digits is 9: \( A + B = 9 \).
2. When 27 is subtracted from the number, the digits are reversed: \( 10A + B - 27 = 10B + A \).

### Step 1: Set up the equations
From the information given, we have two equations:
1. \( A + B = 9 \)
2. \( 10A + B - 27 = 10B + A \)

### Step 2: Simplify the second equation
We can rearrange the second equation to isolate terms involving \( A \) and \( B \):

\[
10A + B - 27 = 10B + A
\]
\[
10A - A + B - 10B = 27
\]
\[
9A - 9B = 27
\]

This simplifies to:

\[
A - B = 3
\]

### Step 3: Solve the system of equations
Now, we have the system:
1. \( A + B = 9 \)
2. \( A - B = 3 \)

We can solve these equations by adding them together:

\[
(A + B) + (A - B) = 9 + 3
\]
\[
2A = 12 \implies A = 6
\]

Now, substitute \( A = 6 \) into the first equation:

\[
6 + B = 9 \implies B = 3
\]

### Step 4: Find the number
The number is formed by \( A \) in the tens place and \( B \) in the units place:

\[
\text{Number} = 10A + B = 10(6) + 3 = 63
\]

### Conclusion
The number is **63**.

Would you like further details on any part of this solution or have additional questions?

Here are 5 related questions:
1. What would happen if the digits sum to a different number?
2. How would the solution change if a different number were subtracted?
3. Can we generalize this problem to a number with more digits?
4. What if the digits were reversed by a different operation instead of subtraction?
5. How can we verify that 63 is indeed the correct answer?

**Tip:** Always double-check your final solution by substituting it back into the original problem conditions.

Learn how to solve a two-digit number problem where the sum of its digits is 9 and when 27 is subtracted from it, the digits are reversed. This problem involves basic algebraic equations and number manipulation techniques suitable for students in Grades 6-8.

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