Apply a given ratio to a known total: A school has 840 students. The ratio of students taking English to those not taking English is 4 : 3. How many students take English?

Introduction / Context: Ratios split a whole into proportional parts. With a total and a two-part ratio, compute the sum of ratio parts to find one-part value, then scale to get the required subgroup size.

Given Data / Assumptions:

• Total students = 840.
• English : Not English = 4 : 3.

Concept / Approach: Total ratio parts = 4 + 3 = 7. One part is 840 / 7. Multiply by the number of parts for the English group to get its headcount.

Step-by-Step Solution:

Verification / Alternative check: Not-English students = 3 * 120 = 360; sum 480 + 360 = 840, which matches the total.

Why Other Options Are Wrong: 360 is the non-English count; 270 and 420 misuse the ratio; 540 exceeds the 4/7 share of 840.

Common Pitfalls: Dividing 840 by 4 or 3 directly; always divide by the sum of ratio parts before scaling.

Final Answer: 480