In a class, the number of boys is 4 times the number of girls. Which of the…
2019
In a class, the number of boys is 4 times the number of girls. Which of the following numbers can represent the total number of students in the class?
Answer: D. 65 — ConceptWhen two groups are in the ratio a:b, their counts can be written as ax and bx for a whole-number scale factor x. Their total is (a + b)x, so every…
- A.
66
- B.
54
- C.
56
- D.
65
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Show answer & explanation
Correct answer: D
Concept
When two groups are in the ratio a:b, their counts can be written as ax and bx for a whole-number scale factor x.
Their total is (a + b)x, so every possible total is a multiple of a + b.
Application
The ratio of girls to boys is 1:4. Let the number of girls be x; then the number of boys is 4x.
The total number of students is x + 4x = 5x. Therefore, the total must be divisible by 5.
Dividing the offered values by 5 gives remainders 1 for 66, 4 for 54, 1 for 56, and 0 for 65.
Cross-check
For 65, x = 65 ÷ 5 = 13. This gives 13 girls and 52 boys; 52 = 4 × 13 and 13 + 52 = 65.
Result
Therefore, 65 can represent the total number of students in the class.