A streaming service charges $8 per month plus a one-time setup fee of $10. Which equation represents the total cost...

1. TRANSLATE the problem information

• Given information:
  • Monthly charge: $8 per month
  • Setup fee: $10 one-time
  • Need total cost c for m months

2. TRANSLATE each cost component

• Monthly charges: $8 per month × m months = \(\mathrm{8m}\) dollars
• Setup fee: $10 (happens once, not per month)
• Total cost: \(\mathrm{c = (monthly\, charges) + (setup\, fee)}\)

3. INFER the final equation structure

• Monthly costs get multiplied by the number of months: \(\mathrm{8m}\)
• One-time fees get added without multiplication: \(\mathrm{+10}\)
• Complete equation: \(\mathrm{c = 8m + 10}\)

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse which cost is "per month" vs "one-time"

They might think the $10 setup fee happens every month, leading to \(\mathrm{c = 10m + 8}\), or they might think the $8 charge is a one-time fee, leading to \(\mathrm{c = 8 + 10m}\). This type of confusion often leads them to select Choice D (\(\mathrm{c = 10m + 8}\)) where they've swapped the coefficients.

Second Most Common Error:

Poor TRANSLATE reasoning: Students correctly identify the components but incorrectly group them with parentheses

They might think "8 per month plus 10 setup" means "8 times (months plus 10)" and write \(\mathrm{c = 8(m + 10)}\). This leads them to select Choice A (\(\mathrm{c = 8(m + 10)}\)).

The Bottom Line:

Success depends on carefully identifying which cost component varies with time (gets multiplied by months) versus which happens once (gets added without multiplication). The key is methodically translating each phrase rather than rushing to an equation.