A father is currently 41 years old. His age equals 5 times his son's age plus some additional years. If...

1. TRANSLATE the problem information

• Given information:
  • Father's current age: 41 years
  • Son's current age: 7 years
  • Father's age equals 5 times son's age plus some additional years

• What this tells us: We need to find how many "additional years" are in this relationship.

2. TRANSLATE the word relationship into an equation

• The key phrase is "His age equals 5 times his son's age plus some additional years"
• Let \(\mathrm{a}\) = the number of additional years
• Mathematical equation: \(\mathrm{Father's\ age = 5 \times (Son's\ age) + additional\ years}\)
• Substituting known values: \(\mathrm{41 = 5(7) + a}\)

3. SIMPLIFY to solve for the unknown

• First, calculate \(\mathrm{5 \times 7 = 35}\)
• Our equation becomes: \(\mathrm{41 = 35 + a}\)
• Subtract 35 from both sides: \(\mathrm{a = 41 - 35 = 6}\)

Answer: C) 6

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret the word relationship and set up an incorrect equation, such as \(\mathrm{41 = 5 \times 7 \times a}\) (thinking "times" means multiply by the additional years) or \(\mathrm{41 = 5 \times (7 + a)}\) (misplacing the additional years inside the parentheses).

When they solve these incorrect equations, they get values that don't match any answer choice, leading to confusion and guessing.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly set up \(\mathrm{41 = 5(7) + a}\) but make arithmetic errors when calculating \(\mathrm{5 \times 7}\) (getting 36 instead of 35) or when subtracting \(\mathrm{41 - 35}\) (getting 7 instead of 6).

An arithmetic error of \(\mathrm{5 \times 7 = 36}\) would give them \(\mathrm{a = 41 - 36 = 5}\), leading them to select Choice B (5).

The Bottom Line:

This problem tests your ability to carefully translate a word relationship into a mathematical equation. The phrase "5 times his son's age plus some additional years" must be interpreted as multiplication first, then addition—not as a single multiplication involving all three quantities.