Solve the Age Equation: If Gabriel is 14 + Simon, When Does Their Total Not Exceed 35?

To solve this problem, we will follow these steps:

• Step 1: Write the equation based on the problem statement.

• Step 2: Simplify and solve the inequality.

• Step 3: Identify the range for Simon's age.

Now, let's work through each step:
Step 1: The problem states that Gabriel is 14 years older than Simon, so if Simon's age is $S$, Gabriel's age is $S + 14$. Given that the sum of their ages does not exceed 35, we can write: $(S) + (S + 14) \leq 35$

Step 2: Simplify the inequality:
$\begin{aligned} 2S + 14 &\leq 35 \\ 2S &\leq 35 - 14 \\ 2S &\leq 21 \end{aligned}$ Divide both sides by 2:
$S \leq 10.5$

Step 3: Given the inequality, Simon’s age is any number greater than or equal to 0 but less than or equal to 10.5. Since Simon must be a whole number, Simon's possible ages range from 0 to 10.

After reviewing the given choices, the correct answer falls within the range:
Between 0 and 10.5