Question:A streaming service charges a one-time activation fee of $52. In addition, the usage fee for the first month is...

1. TRANSLATE the problem information

• Given information:
  • One-time activation fee: $52
  • Usage rate: \(\frac{2}{3}\) dollar per day for first month
  • Days used in first month: 30 days
  • Need: Total cost in dollars

• What this tells us: We have a fixed cost plus a variable cost that depends on usage

2. INFER the approach

• We need to calculate two separate costs and add them together
• Total cost = Fixed activation fee + Variable usage cost
• The usage cost will be: (rate per day) × (number of days)

3. SIMPLIFY the usage cost calculation

• Usage cost = \((\frac{2}{3}) \times 30\)
• Usage cost = \(\frac{2 \times 30}{3} = \frac{60}{3} = 20\)
• So the usage portion costs $20

4. SIMPLIFY to find total cost

• Total cost = Activation fee + Usage cost
• Total cost = \(\$52 + \$20 = \$72\)

Answer: 72

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students focus only on the usage cost and forget about the activation fee entirely.

They calculate \((\frac{2}{3}) \times 30 = 20\) and submit 20 as their final answer, missing that this is only the variable portion of the total cost. The problem structure with both fixed and variable components requires careful attention to all given information.

This leads to the incorrect answer of 20.

Second Most Common Error:

Poor SIMPLIFY execution: Students make arithmetic errors when multiplying the fraction by 30.

They might calculate \((\frac{2}{3}) \times 30\) incorrectly, perhaps getting confused about whether to multiply \(2 \times 30\) first or divide by 3 first. Some students might get \(\frac{60}{3}\) but then make an error calculating that \(60 \div 3 = 20\), instead getting 18 or 22.

This leads to incorrect final answers like 70 or 74.

The Bottom Line:

This problem tests whether students can identify and correctly handle both fixed costs (activation fee) and variable costs (per-day usage) in a real-world scenario. The key challenge is systematic organization - making sure to account for all cost components rather than jumping straight to calculations.