Let's solve this step-by-step.
1. Understand the Problem Statement:
We are given a two-digit number and need to find this number. The number exceeds the sum of its digits by 27. We represent this two-digit number as [tex]\(10x + y\)[/tex], where [tex]\(x\)[/tex] is the tens digit and [tex]\(y\)[/tex] is the units digit.
2. Formulate the Equation:
According to the problem, the two-digit number ([tex]\(10x + y\)[/tex]) exceeds the sum of its digits ([tex]\(x + y\)[/tex]) by 27. This can be formulated into an equation:
[tex]\[
10x + y = (x + y) + 27
\][/tex]
3. Simplify the Equation:
By simplifying the equation:
[tex]\[
10x + y = x + y + 27
\][/tex]
Subtract [tex]\(x + y\)[/tex] from both sides:
[tex]\[
10x + y - x - y = 27
\][/tex]
This simplifies to:
[tex]\[
9x = 27
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{27}{9}
\][/tex]
[tex]\[
x = 3
\][/tex]
5. Determine the Number:
We have found that [tex]\(x\)[/tex], the tens digit, is 3.
Since we are only asked for a specific relationship and weren’t provided additional constraining conditions on [tex]\(y\)[/tex], we assume the simplest case where the units digit [tex]\(y\)[/tex] is 0 to develop the final two-digit number intuitively.
6. Construct the Number:
The two-digit number is [tex]\(10x + y\)[/tex]. With [tex]\(x = 3\)[/tex] and presuming [tex]\(y = 0\)[/tex]:
[tex]\[
10(3) + 0 = 30
\][/tex]
Therefore, the two-digit number is 30.
