The number k is 36% greater than 50. If k is the product of 50 and r, what is the...

1. TRANSLATE the problem information

• Given information:
  • k is 36% greater than 50
  • k is the product of 50 and r
  • Need to find: the value of r

2. TRANSLATE "36% greater than 50" into mathematical form

• "36% greater than" means: original amount + 36% of original amount
• So: \(\mathrm{k = 50 + 36\% \text{ of } 50}\)
• \(\mathrm{k = 50 + 0.36 \times 50 = 50 + 18 = 68}\)

3. INFER the connection between the two expressions for k

• We now know \(\mathrm{k = 68}\)
• We're also told \(\mathrm{k = 50r}\)
• Since both expressions equal k, we can set them equal: \(\mathrm{68 = 50r}\)

4. SIMPLIFY to solve for r

• \(\mathrm{68 = 50r}\)
• \(\mathrm{r = 68/50 = 1.36}\)

Answer: C. 1.36

Why Students Usually Falter on This Problem

Most Common Error Path:

Poor TRANSLATE reasoning: Students misinterpret "36% greater than 50" as simply "36% of 50"

Instead of calculating \(\mathrm{50 + 36\% \text{ of } 50}\), they calculate only \(\mathrm{36\% \text{ of } 50 = 0.36 \times 50 = 18}\). Then they set up \(\mathrm{18 = 50r}\), giving \(\mathrm{r = 18/50 = 0.36}\).

This leads them to select Choice D (0.36) - which the official solution specifically identifies as the result of this exact error.

Second Most Common Error:

Weak INFER skill: Students calculate k correctly as 68 but fail to connect this with the equation \(\mathrm{k = 50r}\)

They might get \(\mathrm{k = 68}\) and then get stuck, not realizing they need to substitute this value into \(\mathrm{50r = k}\). This leads to confusion and guessing among the remaining choices.

The Bottom Line:

The key challenge is correctly translating percentage language - "greater than" requires adding the percentage to the original, not replacing the original with the percentage. This single translation error cascades through the entire solution.