Let's solve this problem step by step.
Step 1: Define Variables
Let's use \( x \) to represent the first number. According to the problem statement, one number is 4 less than 3 times another. This means that the second number can be defined as \( 3x - 4 \).
Step 2: Set Up the Equation
The sum of these two numbers is given as 36. Thus, we have the equation:
\[ x + (3x - 4) = 36 \]
Step 3: Combine Like Terms
Now we simplify the equation by combining like terms, which are the terms containing \( x \):
\[ 4x - 4 = 36 \]
Step 4: Isolate x
In order to solve for \( x \), we should first add 4 to both sides of the equation to isolate the term with x on one side:
\[ 4x - 4 + 4 = 36 + 4 \]
\[ 4x = 40 \]
Now, divide both sides of the equation by 4 to solve for \( x \):
\[ x = \frac{40}{4} \]
\[ x = 10 \]
Step 5: Find the Second Number
Now that we have the value of \( x \), we can find the second number by substituting \( x \) into the expression \( 3x - 4 \):
\[ y = 3x - 4 \]
\[ y = 3(10) - 4 \]
\[ y = 30 - 4 \]
\[ y = 26 \]
Step 6: Verify the Solution
We have found that the first number \( x \) is 10 and the second number \( y \) is 26. We should check to see if these numbers sum up to 36:
\[ x + y = 10 + 26 = 36 \]
The sum does indeed equal 36, which means our solutions for the two numbers are correct.
Therefore, the two numbers are 10 and 26.