A teacher is creating an assignment worth 70 points. The assignment will consist of questions worth 1 point and questions...

1. TRANSLATE the problem information

• Given information:
  • Assignment worth 70 points total
  • \(\mathrm{x}\) = number of 1-point questions
  • \(\mathrm{y}\) = number of 3-point questions

2. INFER how to calculate total points

• The total points come from adding points from both question types
• Each 1-point question contributes 1 point, so x questions contribute \(1 \times \mathrm{x} = \mathrm{x}\) points
• Each 3-point question contributes 3 points, so y questions contribute \(3 \times \mathrm{y} = 3\mathrm{y}\) points

3. TRANSLATE the total into an equation

• Total points = Points from 1-point questions + Points from 3-point questions
• \(70 = \mathrm{x} + 3\mathrm{y}\)
• Therefore: \(\mathrm{x} + 3\mathrm{y} = 70\)

Answer: D. \(\mathrm{x} + 3\mathrm{y} = 70\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students mix up which coefficient belongs with which variable type.

They might think: "1-point questions = x, so that's 1x... but wait, there are 3-point questions too, so maybe it's 3x?" This leads them to write \(3\mathrm{x} + \mathrm{y} = 70\), reversing the coefficients.

This may lead them to select Choice C (\(3\mathrm{x} + \mathrm{y} = 70\)).

Second Most Common Error:

Poor INFER reasoning: Students don't understand how to combine different point values properly.

They might think: "There are 1-point and 3-point questions, so together that's 4 points total" and try to multiply by (x + y), leading to \(4(\mathrm{x} + \mathrm{y}) = 70\).

This may lead them to select Choice B (\(4(\mathrm{x} + \mathrm{y}) = 70\)).

The Bottom Line:

Success requires carefully TRANSLATING each part of the problem (matching point values to their corresponding variables) and INFERRING that total points come from adding, not multiplying, the contributions from each question type.