A museum rents tablets to visitors. The museum earns revenue of $14 for each tablet rented for the day. On...

1. TRANSLATE the problem information

• Given information:
  • Revenue per tablet rented = \(\$14\)
  • Profit earned on Wednesday = \(\$406\)
  • Daily expenses = \(\$112\)
  • Formula provided: profit = total revenue - total expenses
• What we need to find: number of tablets rented on Wednesday

2. TRANSLATE the unknown and revenue

• Let \(\mathrm{x}\) = number of tablets rented on Wednesday
• Total revenue = \(14\mathrm{x}\) (since each tablet generates \(\$14\) revenue)

3. INFER the equation setup

• We know: profit = total revenue - total expenses
• Substituting our values: \(406 = 14\mathrm{x} - 112\)
• This equation represents the Wednesday situation

4. SIMPLIFY the equation

• Start with: \(406 = 14\mathrm{x} - 112\)
• Add 112 to both sides: \(406 + 112 = 14\mathrm{x}\)
• Calculate: \(518 = 14\mathrm{x}\)
• Divide both sides by 14: \(\mathrm{x} = 518 \div 14 = 37\)

Answer: 37

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students misinterpret the relationship between the given quantities, often setting up incorrect equations like \(406 = 14\mathrm{x} + 112\) (adding expenses instead of subtracting) or \(14\mathrm{x} = 406 + 112\) (forgetting about expenses entirely).

The confusion often stems from not carefully parsing "earned \(\$406\) in profit AFTER paying daily expenses." They might think expenses are additional earnings rather than deductions from revenue.

This leads to incorrect calculations and wrong final answers.

Second Most Common Error:

Inadequate SIMPLIFY execution: Students correctly set up \(406 = 14\mathrm{x} - 112\) but make arithmetic errors when solving, such as:

• Incorrectly calculating \(406 + 112 = 518\)
• Making division errors: \(518 \div 14\)
• Forgetting to perform operations on both sides of the equation

These calculation mistakes lead to answers other than 37.

The Bottom Line:

This problem requires careful reading to distinguish between revenue, profit, and expenses, then systematic algebraic manipulation. Students who rush through the translation step or make computational errors will struggle to reach the correct answer.