Question

Sarah's current age is three times Ron's age two years ago. Sarah is currently 14 years older than Ron. What is the sum of Sarah and Ron's current age?

• A. 24
• B. 36
• C. 34
• D. 32
• E.

Hint:

For age problems, always define your variables clearly (e.g., "let R be Ron's *current* age"). Pay close attention to phrases like "two years ago" or "in five years" and adjust the variable accordingly (R-2 or R+5).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a word problem about ages that can be solved by setting up a system of two linear equations with two variables.
Step 2: Key Formula or Approach:
Let S be Sarah's current age and R be Ron's current age. Translate the given information into equations: 1. "Sarah's current age is three times Ron's age two years ago": \( S = 3(R - 2) \) 2. "Sarah is currently 14 years older than Ron": \( S = R + 14 \) We need to solve for S and R, and then find their sum.
Step 3: Detailed Explanation:
We have a system of two equations for S: \[ S = 3R - 6 \] \[ S = R + 14 \] Since both expressions are equal to S, we can set them equal to each other: \[ 3R - 6 = R + 14 \] Now, solve for R. Subtract R from both sides: \[ 2R - 6 = 14 \] Add 6 to both sides: \[ 2R = 20 \] \[ R = 10 \] So, Ron's current age is 10. Now find Sarah's age using the simpler equation: \[ S = R + 14 = 10 + 14 = 24 \] Sarah's current age is 24. The question asks for the sum of their current ages: \[ S + R = 24 + 10 = 34 \] Step 4: Final Answer:
The sum of Sarah and Ron's current age is 34.