Question: Example 2: One number is 3 less than another number. If the sum of the two numbers is 177, find each number.
1. **State the problem:** We need to find two numbers where one number is 3 less than the other, and their sum is 177.
2. **Define variables:** Let $x$ be the second number.
3. **Express the first number:** Since one number is 3 less than the other, the first number is $x - 3$.
4. **Write the equation for the sum:** The sum of the two numbers is given as $$ (x) + (x - 3) = 177 $$
5. **Simplify the equation:**
$$ x + x - 3 = 177 $$
$$ 2x - 3 = 177 $$
6. **Isolate the variable term:**
$$ 2x - 3 + 3 = 177 + 3 $$
$$ 2x = 180 $$
7. **Solve for $x$ by dividing both sides by 2:**
$$ \frac{\cancel{2}x}{\cancel{2}} = \frac{180}{2} $$
$$ x = 90 $$
8. **Find the first number:**
$$ x - 3 = 90 - 3 = 87 $$
9. **Answer:** The two numbers are $87$ and $90$.