The equation x + y = 1{,440} represents the number of minutes of daylight (between sunrise and sunset), x, and...

1. TRANSLATE the problem information

• Given information:
  • Equation: \(\mathrm{x + y = 1,440}\) (total minutes in a day)
  • \(\mathrm{x}\) = minutes of daylight = 670
  • \(\mathrm{y}\) = minutes of non-daylight (what we need to find)

2. SIMPLIFY by substitution and solving

• Substitute the known value \(\mathrm{x = 670}\) into the equation:
  \(\mathrm{670 + y = 1,440}\)

• Solve for \(\mathrm{y}\) by subtracting 670 from both sides:
  \(\mathrm{y = 1,440 - 670}\)
  \(\mathrm{y = 770}\)

Answer: B. 770

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misread what the problem is asking for and select the given daylight minutes instead of calculating non-daylight minutes.

They see "670 minutes of daylight" in the problem and immediately select this value without recognizing that the question asks for non-daylight minutes. This leads them to select Choice A (670).

Second Most Common Error:

Poor SIMPLIFY execution: Students make arithmetic errors during the subtraction, often dropping a digit from 670.

When calculating \(\mathrm{1,440 - 670}\), they might accidentally compute \(\mathrm{1,440 - 67 = 1,373}\), leading them to select Choice C (1,373).

The Bottom Line:

This problem tests careful reading comprehension and basic algebraic substitution. Success requires distinguishing between what's given (daylight minutes) and what's asked for (non-daylight minutes), then executing straightforward equation solving.