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Difficulty: EasyRatios, Rates, and Proportions

In a school club of 4040 students, the ratio of the number of boys to the number of girls is 3:53 : 5. Which of the following statements must be true? Select all such statements.

  1. The number of boys in the club is 1515.Answer
  2. The ratio of the number of boys to the total number of students is 3:83 : 8.Answer
  3. The number of girls in the club exceeds the number of boys by 1010.Answer
  4. D
    The ratio of the number of boys to the total number of students is 3:53 : 5.
  5. E
    The number of girls in the club is 2020.

Answer

The correct statements are those indicating that there are 15 boys in the club, that the ratio of boys to total students is 3:8, and that there are 10 more girls than boys in the club.
The total number of ratio parts is 3+5=83 + 5 = 8, representing the entire group of 4040 students. Dividing 4040 by 88 gives 55 students per part. Therefore, the number of boys is 3×5=153 \times 5 = 15, the number of girls is 5×5=255 \times 5 = 25, and the ratio of boys to total students is 15:40=3:815:40 = 3:8. Subtracting the number of boys from girls (25−15=1025 - 15 = 10) shows there are 1010 more girls than boys.

Step-by-Step Solution

1
Calculate total ratio parts and determine the value of one part.
Total ratio parts = 3+5=83 + 5 = 8. Each part corresponds to 408=5\frac{40}{8} = 5 students.
Converting ratio terms into parts allows calculation of actual quantities from the total group size.
2
Compute the total number of boys and girls.
Number of boys = 3×5=153 \times 5 = 15. Number of girls = 5×5=255 \times 5 = 25.
Multiply each component's ratio share by the value of one part.
3
Evaluate the given statements against calculated quantities.
There are 1515 boys; the ratio of boys to total students is 15:40=3:815:40 = 3:8; and the difference between girls and boys is 25−15=1025 - 15 = 10.
Determines which options represent true statements about the group.

Key Concept

Part-to-Part vs. Part-to-Whole Ratios
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Topics

Ratios, Rates, and Proportions

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