At a construction site, safety regulations require that the ratio of supervisors to workers be maintained at 1:15. If there...

1. TRANSLATE the problem information

• Given information:
  • Ratio of supervisors to workers = \(\mathrm{1:15}\)
  • There are n supervisors at the site
• Find: Expression for number of workers needed

2. INFER what the ratio means

• A ratio of \(\mathrm{1:15}\) means: for every 1 supervisor, there must be 15 workers
• This is a multiplication relationship, not addition
• If 1 supervisor \(\mathrm{\rightarrow}\) 15 workers, then n supervisors \(\mathrm{\rightarrow}\) ? workers

3. TRANSLATE this understanding into an expression

• Since each supervisor needs 15 workers:
• Number of workers = \(\mathrm{15 \times (number\:of\:supervisors)}\)
• Number of workers = \(\mathrm{15 \times n = 15n}\)

Answer: B. \(\mathrm{15n}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret what "ratio of \(\mathrm{1:15}\)" means in practical terms. They might think this means "1 supervisor plus 15 workers" or get confused about which quantity gets multiplied.

This reasoning leads them to select Choice C (\(\mathrm{n + 15}\)), thinking you just add 15 workers to n supervisors.

Second Most Common Error:

Poor INFER reasoning: Students understand there's a relationship but get the direction backwards. They think "if the ratio is \(\mathrm{1:15}\), then n supervisors means \(\mathrm{\frac{n}{15}}\) workers" - essentially thinking about how many supervisor groups you have instead of how many workers each supervisor needs.

This may lead them to select Choice A (\(\mathrm{\frac{n}{15}}\)).

The Bottom Line:

Ratio problems require understanding both the language ("\(\mathrm{1:15}\)") and the mathematical operation (multiplication, not addition). The key insight is recognizing that ratios describe scaling relationships.