In August, a car dealer completed 15 more than 3 times the number of sales the car dealer completed in...

1. TRANSLATE the problem information

• Given information:
  • August sales = 15 more than 3 times September sales
  • Total sales (August + September) = 363 sales
  • Need to find: September sales

• What this tells us: We need to express both months' sales in terms of one variable

2. TRANSLATE the relationships into mathematical expressions

• Let \(\mathrm{x}\) = September sales
• August sales = \(\mathrm{3x + 15}\) (this captures "15 more than 3 times September")
• Total equation: \(\mathrm{x + (3x + 15) = 363}\)

3. SIMPLIFY to solve the equation

• Combine like terms: \(\mathrm{4x + 15 = 363}\)
• Subtract 15 from both sides: \(\mathrm{4x = 348}\)
• Divide by 4: \(\mathrm{x = 87}\)

Answer: 87

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students often misinterpret "15 more than 3 times the number" and set up the wrong expression for August sales.

They might write August = \(\mathrm{3x - 15}\) (thinking "15 less than") or August = \(\mathrm{3(x + 15)}\) (thinking "3 times the sum"). With August = \(\mathrm{3x - 15}\), their equation becomes \(\mathrm{x + (3x - 15) = 363}\), leading to \(\mathrm{4x - 15 = 363}\), so \(\mathrm{4x = 378}\), and \(\mathrm{x = 94.5}\). Since this isn't among typical answer choices, this leads to confusion and guessing.

The Bottom Line:

The key challenge is accurately translating the phrase "15 more than 3 times" into the expression \(\mathrm{3x + 15}\). Students must carefully parse the order of operations in word problems to set up correct mathematical relationships.