Boys to girls ratio from a percent relation: In a school, 10% of the boys equals one-fourth of the girls. What is the ratio of boys to girls?

Introduction / Context:We translate a sentence connecting percentages of groups into an algebraic relation to obtain a ratio.

Given Data / Assumptions:

• B = number of boys; G = number of girls.
• 10% of boys = one-fourth of girls ⇒ 0.10B = 0.25G.

Concept / Approach:Rearrange to B/G by isolating terms.

Step-by-Step Solution:

Verification / Alternative check:Pick numbers matching 5 : 2, e.g., B = 50, G = 20. Then 10% of boys = 5; one-fourth of girls = 5. Condition satisfied.

Why Other Options Are Wrong:

• 3 : 2, 2 : 1, 4 : 3, 5 : 3 do not satisfy 0.10B = 0.25G.

Common Pitfalls:Inverting the ratio (2 : 5) or mixing percent with fraction improperly.

Final Answer:5 : 2