Connor has c dollars and Maria has m dollars. Connor has 4 times as many dollars as Maria, and together...

1. TRANSLATE the problem information

• Given information:
  • Connor has c dollars, Maria has m dollars
  • "Connor has 4 times as many dollars as Maria"
  • "together they have a total of $25.00"

2. TRANSLATE each relationship into an equation

• "Connor has 4 times as many dollars as Maria":
  This means Connor's amount = 4 × Maria's amount
  So: \(\mathrm{c = 4m}\)

• "together they have a total of $25.00":
  This means Connor's amount + Maria's amount = 25
  So: \(\mathrm{c + m = 25}\)

3. INFER that we need both equations together

• Since both conditions must be true at the same time, we need a system of equations:
  \(\mathrm{c = 4m}\)
  \(\mathrm{c + m = 25}\)

4. Match with answer choices

Looking at the options, Choice A gives us exactly \(\mathrm{c = 4m}\) and \(\mathrm{c + m = 25}\).

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "Connor has 4 times as many dollars as Maria" and write \(\mathrm{m = 4c}\) instead of \(\mathrm{c = 4m}\).

The phrase "Connor has 4 times as many" means Connor's amount equals 4 times Maria's amount, but students sometimes think it means Maria has 4 times Connor's amount. They get the relationship backwards.

This may lead them to select Choice B (\(\mathrm{m = 4c}\), \(\mathrm{c + m = 25}\)).

Second Most Common Error:

Poor TRANSLATE reasoning: Students mix up which numbers go where, potentially writing equations like \(\mathrm{c = 25m}\) or interpreting the total as $4 instead of $25.

This confusion about which numbers represent the multiplier versus the total can cause them to get stuck and guess, or select Choice C or Choice D.

The Bottom Line:

The key challenge is carefully translating "X has [number] times as many as Y" into the correct equation \(\mathrm{X = [number] \times Y}\), not the reverse. Students must slow down and think about which variable should equal the multiple of the other.