At a conference, a coordinator schedules s short talks, each lasting 20 minutes, and l long talks, each lasting 50...

1. TRANSLATE the problem information

• Given information:
  • \(\mathrm{s}\) = number of short talks (unknown)
  • \(\mathrm{l}\) = number of long talks (unknown)
  • Each short talk = \(\mathrm{20}\) minutes
  • Each long talk = \(\mathrm{50}\) minutes
  • Total scheduled time = \(\mathrm{440}\) minutes

2. INFER how to find total time

• The total time comes from adding contributions of both talk types
• Each talk type contributes: (number of talks) × (time per talk)
• So we need: (short talk time) + (long talk time) = total time

3. TRANSLATE each contribution into math

• Short talks contribute: \(\mathrm{s}\) talks × \(\mathrm{20}\) minutes each = \(\mathrm{20s}\) minutes
• Long talks contribute: \(\mathrm{l}\) talks × \(\mathrm{50}\) minutes each = \(\mathrm{50l}\) minutes
• Total equation: \(\mathrm{20s + 50l = 440}\)

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students don't recognize that they need to multiply the number of talks by the duration per talk.

Instead, they might think the equation should just count the talks themselves: \(\mathrm{s + l = 440}\). This treats the variables as if they represent minutes rather than number of talks, ignoring that different talks have different durations.

This may lead them to select Choice A (\(\mathrm{s + l = 440}\)).

Second Most Common Error:

Incomplete TRANSLATE reasoning: Students correctly identify that short talks contribute \(\mathrm{20s}\) minutes, but incorrectly think long talks just contribute \(\mathrm{l}\) minutes instead of \(\mathrm{50l}\) minutes.

This creates the equation \(\mathrm{20s + l = 440}\), mixing time units (\(\mathrm{20s}\) in minutes) with count units (\(\mathrm{l}\) as number of talks).

This may lead them to select Choice B (\(\mathrm{20s + l = 440}\)).

The Bottom Line:

This problem requires careful attention to units and what each variable represents. Success depends on systematically translating each part: "\(\mathrm{s}\) short talks at \(\mathrm{20}\) minutes each" becomes "\(\mathrm{20s}\) minutes total from short talks."