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Difficulty: EasyRatios, Rates, and Proportions

A class of 4040 students has a ratio of boys to girls of 3:53:5. How many more girls than boys are in the class?

  1. A
    5
  2. B
    8
  3. 10Answer
  4. D
    15
  5. E
    25

Answer

There are 10 more girls than boys in the class.
To find the difference between the number of girls and boys, we first determine the value of one part of the ratio. Since the ratio of boys to girls is 3:53:5, there are 3+5=83 + 5 = 8 total parts. With 4040 students in total, each part corresponds to 40÷8=540 \div 8 = 5 students. The difference between the ratio parts is 5−3=25 - 3 = 2 parts. Multiplying this difference by the value of one part gives 2×5=102 \times 5 = 10 more girls than boys.

Step-by-Step Solution

1
Find the total number of parts in the ratio by adding the parts for boys and girls.
3+5=83 + 5 = 8 parts
To determine how the total number of students is divided, we need the sum of the ratio parts.
2
Calculate how many students represent one part of the ratio by dividing the total number of students by the total parts.
40÷8=540 \div 8 = 5 students per part
This establishes the scale factor for the ratio to convert parts into actual student counts.
3
Find the difference in ratio parts between girls and boys.
5−3=25 - 3 = 2 parts
The question asks for the difference in the number of girls and boys, which corresponds to the difference in their ratio parts.
4
Multiply the difference in parts by the number of students per part.
2×5=102 \times 5 = 10 students
This gives the final difference in the number of girls and boys.

Key Concept

Solving part-to-part ratio problems using total quantities

Alternative Method

Alternatively, calculate the actual number of boys and girls first. The number of boys is 38×40=15\frac{3}{8} \times 40 = 15 and the number of girls is 58×40=25\frac{5}{8} \times 40 = 25. Subtracting the number of boys from the number of girls yields 25−15=1025 - 15 = 10.
Estimated Time:45s
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Topics

Ratios, Rates, and Proportions

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