Two banana bunches: the first has “one-quarter again as many” as the second, and the second has 3 fewer than the first. How many bananas are in the first bunch?

Introduction / Context:This is an algebraic word problem involving proportional language. “One-quarter again as many” means the first quantity equals the second plus one-quarter of the second (i.e., 125% of the second). We also have a difference statement linking the two counts.

Given Data / Assumptions:

• Let F = number of bananas in the first bunch.
• Let S = number of bananas in the second bunch.
• “First has one-quarter again as many as second” means F = (5/4) * S.
• “Second has 3 less than first” means S = F - 3.

Concept / Approach:Translate the English phrases into equations, then solve the simultaneous system. Substitute one equation into the other to find the exact integer values that satisfy both conditions.

Step-by-Step Solution:

Verification / Alternative check:Compute S: S = F - 3 = 12. Check “one-quarter again as many”: (5/4) * 12 = 15. Both conditions hold perfectly.

Why Other Options Are Wrong:

• 9, 10, 12 — none satisfy both the proportional and difference constraints simultaneously.

Common Pitfalls:Misreading “one-quarter again as many” as “one-quarter as many.” The word “again” indicates adding the fraction to the whole: 1 + 1/4 = 5/4.

Final Answer:15