An online retailer charges a one-time membership fee of $25 and $14 for each order placed. If Priya places n...

1. TRANSLATE the problem information

• Given information:
  • One-time membership fee: \(\$25\) (paid once, regardless of orders)
  • Cost per order: \(\$14\) (paid for each order)
  • Number of orders: n (variable)
  • Total amount spent: \(\$165\)
• What this tells us: We have a fixed cost plus a variable cost that depends on the number of orders.

2. INFER the mathematical relationship

• Total spending = Fixed cost + Variable cost
• The membership fee (\(\$25\)) is paid once, so it's just 25
• The order cost (\(\$14\)) is paid n times, so it's 14n
• Therefore: Total spending = \(25 + 14\mathrm{n}\)

3. Set up the equation

• We know the total spending is \(\$165\)
• So: \(25 + 14\mathrm{n} = 165\)
• This can be written as: \(14\mathrm{n} + 25 = 165\)

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse which cost is fixed vs variable, thinking the \(\$25\) membership fee applies to each order rather than being a one-time cost.

This leads them to write: \(\$25\) per order × n orders + \(\$14\) fixed = \(25\mathrm{n} + 14 = 165\)

This may lead them to select Choice D (\(25\mathrm{n} + 14 = 165\))

Second Most Common Error:

Poor TRANSLATE reasoning: Students correctly identify the costs but use subtraction instead of addition, perhaps thinking they need to "subtract out" the membership fee from the total.

This creates the equation: \(14\mathrm{n} - 25 = 165\)

This may lead them to select Choice A (\(14\mathrm{n} - 25 = 165\))

The Bottom Line:

The key challenge is carefully reading to distinguish between one-time costs (membership fee) and per-unit costs (cost per order), then correctly adding these components rather than subtracting or mixing up which is which.