School enrollment ratio problem: The total number of students in a school is 2140. If 1200 are girls, how many are boys, and what is the simplified ratio of boys to girls?

Introduction / Context:
This is a foundational ratio-and-proportion question that asks you to convert counts into a simplified ratio. You must first find the number of boys, then reduce the ratio of boys to girls to lowest terms.

Given Data / Assumptions:

• Total students = 2140.
• Girls = 1200.
• Boys = Total − Girls.
• Ratio required = Boys : Girls in simplest form.

Concept / Approach:
Ratios compare two quantities by division. After computing the absolute number of boys, form the ratio Boys : Girls and divide both terms by their greatest common divisor (GCD) to simplify.

Step-by-Step Solution:
Boys = 2140 − 1200 = 940.Raw ratio = 940 : 1200.Divide both by 20 (a common factor): 940/20 : 1200/20 = 47 : 60.

Verification / Alternative check:
Check divisibility again: 47 is prime and does not divide 60; hence 47 : 60 is already in lowest terms.

Why Other Options Are Wrong:

• 26 : 25 corresponds to unequal totals and does not match 940 : 1200.
• 18 : 13 is not proportional to 940 : 1200.
• 31 : 79 inverts the relative sizes; girls exceed boys here.

Common Pitfalls:

• Forgetting to compute boys as the remainder after removing girls from the total.
• Not simplifying the ratio fully to lowest terms.

Final Answer:
47 : 60