Question

Frank is 15 years younger than John. In 5 years John will be twice as old as Frank. How old will Frank be in four years?

• A. 8
• B. 10
• C. 12
• D. 14
• E. 16

Hint:

In age-related word problems, carefully distinguish between current ages, past ages, and future ages. Always define your variables clearly (e.g., F = Frank's *current* age) and read the final question carefully to ensure you are solving for the correct value.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This is a word problem that can be solved by setting up a system of linear equations based on the age relationships described.
Step 2: Detailed Explanation:
Part 1: Define variables and set up equations
Let F be Frank's current age.
Let J be John's current age.
From the first sentence: "Frank is 15 years younger than John."
\[ F = J - 15 \quad \text{or} \quad J = F + 15 \quad \text{(Equation 1)} \] Now, consider their ages in 5 years:
Frank's age in 5 years = F + 5.
John's age in 5 years = J + 5.
From the second sentence: "In 5 years John will be twice as old as Frank."
\[ J + 5 = 2(F + 5) \quad \text{(Equation 2)} \] Part 2: Solve the system of equations
Substitute Equation 1 into Equation 2 to eliminate J.
\[ (F + 15) + 5 = 2(F + 5) \] Simplify both sides of the equation.
\[ F + 20 = 2F + 10 \] Now, solve for F by isolating the variable.
\[ 20 - 10 = 2F - F \] \[ 10 = F \] So, Frank's current age is 10 years. Part 3: Answer the specific question
The question asks for Frank's age in four years, not his current age.
\[ \text{Frank's age in 4 years} = \text{Current age} + 4 \] \[ \text{Frank's age in 4 years} = 10 + 4 = 14 \] Step 3: Final Answer
In four years, Frank will be 14 years old.