Careful with fractions in word problems: In an exam, a student was asked to compute 3/14 of a certain number N, but by mistake he computed 3/4 of N. His (wrong) answer was 150 greater than the correct answer. What is the value of N?

Introduction / Context:
This is a straightforward linear equation framed in words. It tests converting “more than” into a difference of fractional multiples and solving for the base number. Precision with common denominators is vital.

Given Data / Assumptions:

• Correct value should be (3/14) * N.
• Mistake value computed was (3/4) * N.
• Difference (mistake − correct) equals 150.

Concept / Approach:
Model the statement as ((3/4) − (3/14)) * N = 150. Reduce the fractional difference, then isolate N. Avoid mixing decimals to keep exactness.

Step-by-Step Solution:
Compute the difference: 3/4 − 3/14 = (42 − 12)/56 = 30/56 = 15/28.Equation: (15/28) * N = 150.Solve for N: N = 150 * (28/15) = 10 * 28 = 280.

Verification / Alternative check:
Correct: (3/14) * 280 = 60. Mistake: (3/4) * 280 = 210. Difference: 210 − 60 = 150, consistent.

Why Other Options Are Wrong:
180, 240, and 196 yield differences other than 150; 290 is not a nice multiple that satisfies the derived equation.

Common Pitfalls:
Reversing the order of subtraction; mishandling 3/14; prematurely rounding; skipping fraction reduction before solving.

Final Answer:
280