Question

If Leah is 6 years older than Sue, and John is 5 years older than Leah, and the total of their ages is 41. Then how old is Sue?

• A. 8
• B. 10
• C. 14
• D. 19
• E. 21

Hint:

After solving, it's a good practice to check your answer. If Sue is 8, Leah is 8+6=14, and John is 14+5=19. Their total age is 8+14+19=41, which matches the problem statement.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a word problem that can be solved by setting up an algebraic equation based on the relationships between the ages.
Step 2: Key Formula or Approach:
1. Define a variable for the unknown age (Sue's age).
2. Express the other ages in terms of this variable.
3. Set up an equation where the sum of the ages equals the given total.
4. Solve the equation for the variable.
Step 3: Detailed Explanation:
Let S be Sue's age.
Leah (L) is 6 years older than Sue, so: \[ L = S + 6 \] John (J) is 5 years older than Leah, so: \[ J = L + 5 = (S + 6) + 5 = S + 11 \] The sum of their ages is 41: \[ S + L + J = 41 \] Now, substitute the expressions for L and J into the sum equation: \[ S + (S + 6) + (S + 11) = 41 \] Combine the like terms: \[ 3S + 17 = 41 \] Subtract 17 from both sides: \[ 3S = 41 - 17 \] \[ 3S = 24 \] Divide by 3 to find S: \[ S = \frac{24}{3} = 8 \] Step 4: Final Answer:
Sue is 8 years old. The correct option is (A).