If the numerator of a fraction is increased by 200% and the denominator is increased by 150%, the resulting fraction is 9/35. What was the original fraction?

Introduction / Context: Percentage changes to numerator and denominator scale a fraction by separate multipliers. Translate the described changes into factors and solve for the original fraction.

Given Data / Assumptions:

• Original fraction = x / y.
• Numerator +200% ⇒ new numerator = 3x.
• Denominator +150% ⇒ new denominator = 2.5y.
• New fraction = 9/35.

Concept / Approach: Form the equation (3x)/(2.5y) = 9/35. Simplify the coefficient 3/2.5 to 6/5 or 3/(5/2). Solve for x/y and reduce to lowest terms.

Step-by-Step Solution:

Verification / Alternative check: Starting from 3/14: New value = (3*3)/(14*2.5) = 9/35 as required.

Why Other Options Are Wrong: 3/10, 2/15, 2/7 do not transform to 9/35 under the stated multipliers.

Common Pitfalls: Treating 200% increment as 2x instead of 3x, or 150% increment as 1.5y instead of 2.5y.

Final Answer: 3/14