A school has 8,670 students. If boys are 4,545, find the ratio of boys to girls in simplest terms.

Introduction / Context:
We compute girls from the total and then reduce the ratio boys : girls to lowest terms.

Given Data / Assumptions:
Total = 8,670; Boys = 4,545; Girls = Total − Boys.

Concept / Approach:
Find girls, then simplify the ratio using a common divisor.

Step-by-Step Solution:
Girls = 8,670 − 4,545 = 4,125. Boys : Girls = 4,545 : 4,125. Divide both by 15: 4,545/15 = 303; 4,125/15 = 275. Simplified ratio = 303 : 275.

Verification / Alternative check:
Compute 303*15 = 4,545 and 275*15 = 4,125, confirming the reduction.

Why Other Options Are Wrong:
275 : 303 inverts; 11 : 12 and 12 : 11 do not match the exact counts.

Common Pitfalls:
Arithmetic mistakes when subtracting or simplifying by the wrong common divisor.

Final Answer:
303 : 275