Given the ratio of boys to girls is 3:4 and there are 21 boys, what is the total number of students?

• A. 49
• B. 42
• C. 56
• D. 63

Answer: (A)

In this kind of problem, you’re using ratios to split a total into equal parts. A ratio of 3:4 means the whole group is made of 3 parts for boys and 4 parts for girls, totaling 7 equal parts.

The 21 boys correspond to 3 parts, so one part equals 21 divided by 3, which is 7. The girls then occupy 4 parts, which is 4 × 7 = 28 girls. The total number of students is 21 plus 28, giving 49.

If the total were different, the size of each part would change and the number of boys would no longer be 21. For example, with a total of 42, each part would be 6 (giving 3×6 = 18 boys); with 56, each part would be 8 (giving 24 boys); with 63, each part would be 9 (giving 27 boys). Only 49 keeps the boys at 21.