The equation (x + y)/2 = 720 represents the average of two math test scores, x and y. If one...

1. TRANSLATE the problem information

• Given information:
  • The average of two test scores x and y equals 720: \(\frac{\mathrm{x} + \mathrm{y}}{2} = 720\)
  • One test score is 584

• What this tells us: We can substitute the known value and solve for the unknown score.

2. TRANSLATE by substituting the known value

• Since one test score is 584, substitute this into our equation:
  \(\frac{584 + \mathrm{y}}{2} = 720\)

• Now we have a linear equation with one unknown.

3. SIMPLIFY to solve for the unknown score

• Multiply both sides by 2 to eliminate the fraction:
  \(584 + \mathrm{y} = 1440\)

• Subtract 584 from both sides:
  \(\mathrm{y} = 1440 - 584 = 856\)

Answer: B (856)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may not recognize that they should substitute the known value into the average formula, instead trying to work with the abstract equation \(\frac{\mathrm{x} + \mathrm{y}}{2} = 720\) without using the given information that one score is 584.

This leads to confusion about how to proceed and often results in guessing rather than systematic solution.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly set up \(\frac{584 + \mathrm{y}}{2} = 720\) but make arithmetic errors, particularly when calculating \(1440 - 584\). Common calculation mistakes include getting 864 instead of 856, or other computational errors.

This may lead them to select Choice A (136) if they incorrectly calculate or get confused about the direction of the subtraction.

The Bottom Line:

This problem tests whether students understand that knowing one piece of information (one test score) allows them to work backwards from the average to find the missing piece. The key insight is recognizing that the average formula becomes a simple linear equation once you substitute known values.