Question:A number n is decreased by 5, and then the result is multiplied by 3. The final value is 21....

1. TRANSLATE the problem information step by step

The key is to convert each part in the exact order given:

• "A number n is decreased by 5" → \(\mathrm{n - 5}\)
• "then the result is multiplied by 3" → \(\mathrm{3(n - 5)}\)
• "The final value is 21" → \(\mathrm{= 21}\)

Important: The word "then" tells us the order matters!

2. INFER why order and parentheses matter

• The parentheses in \(\mathrm{3(n - 5)}\) ensure we subtract 5 first, then multiply the entire result by 3
• Without parentheses, \(\mathrm{3n - 5}\) would multiply n by 3 first, then subtract 5 (different meaning)

3. TRANSLATE this into the complete equation

Putting it all together: \(\mathrm{3(n - 5) = 21}\)

4. Verify by checking each answer choice

• (A) \(\mathrm{3n - 5 = 21}\) multiplies first, subtracts second (wrong order)
• (B) \(\mathrm{3(n - 5) = 21}\) matches our translation (correct)
• (C) \(\mathrm{n - 5 \cdot 3 = 21}\) means \(\mathrm{n - 15 = 21}\) (only 5 gets multiplied)
• (D) \(\mathrm{(n - 5) + 3 = 21}\) uses addition instead of multiplication

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students translate piece by piece but ignore the sequential order indicated by "then"

They might think: "n decreased by 5 is n-5, and multiply by 3 is times 3, so it's 3n - 5 = 21"

This leads them to select Choice A (\(\mathrm{3n - 5 = 21}\))

Second Most Common Error:

Poor TRANSLATE reasoning: Students misunderstand what "the result is multiplied by 3" refers to

They think the 5 gets multiplied by 3, creating n - 5×3, which becomes n - 15 = 21

This may lead them to select Choice C (\(\mathrm{n - 5 \cdot 3 = 21}\))

The Bottom Line:

The word "then" is crucial - it tells you that one operation must be completed before the next one begins. This is why we need parentheses to group \(\mathrm{(n - 5)}\) together before multiplying by 3.