What value of p satisfies the equation 2p + 275 = 325?

1. INFER the solution strategy

• Goal: Isolate p by getting it alone on one side
• Strategy: Use inverse operations to "undo" what's being done to p
• Since p is multiplied by 2, then 275 is added, we'll reverse these operations

2. SIMPLIFY by removing the added term first

• Starting equation: \(\mathrm{2p + 275 = 325}\)
• Subtract 275 from both sides: \(\mathrm{2p + 275 - 275 = 325 - 275}\)
• This gives us: \(\mathrm{2p = 50}\)

3. SIMPLIFY by removing the coefficient

• Now we have: \(\mathrm{2p = 50}\)
• Divide both sides by 2: \(\mathrm{2p/2 = 50/2}\)
• This gives us: \(\mathrm{p = 25}\)

Answer: B. 25

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students may not recognize the correct order of operations to isolate p, or they may apply operations to only one side of the equation.

Some students subtract 275 from only the right side, getting \(\mathrm{2p + 275 = 50}\), then become confused about what to do next. Others might divide by 2 first instead of subtracting 275, leading to complicated fractions. This leads to confusion and guessing.

Second Most Common Error:

Poor SIMPLIFY execution: Students misread the original equation structure, solving a different equation instead.

For example, reading "\(\mathrm{2p + 275 = 325}\)" as "\(\mathrm{(2 + p) + 275 = 325}\)" leads them to solve \(\mathrm{2 + p = 50}\), giving \(\mathrm{p = 48}\). This may lead them to select Choice C (48). Similarly, misreading as "\(\mathrm{2p - 275 = 325}\)" gives \(\mathrm{p = 300}\), leading to Choice D (300).

The Bottom Line:

This problem tests whether students can systematically apply inverse operations in the correct order while maintaining equation balance - a fundamental skill for all algebraic problem-solving.