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The ratio of boys to girls in the junior class is 2 to 3 respectively and the ratio of girls to boys in the senior class is 7 to 3 respectively. If there are 300 more students in the senior class than in the junior class and the combined ratio of boys to girls in both classes is 8 to 17 respectively, how many students are in the senior class?
  • a)
    100
  • b)
    300
  • c)
    375
  • d)
    400
  • e)
    500
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The ratio of boys to girls in the junior class is 2 to 3 respectively ...
Understanding the Problem
To solve the problem, we need to define variables for the number of boys and girls in both classes and set up equations based on the given ratios.
Defining Variables
- Let the number of boys in the junior class be 2x.
- Let the number of girls in the junior class be 3x.
- Thus, the total number of students in the junior class is:
Total_Junior = 2x + 3x = 5x
- For the senior class:
- Let the number of girls be 7y.
- Let the number of boys be 3y.
- Thus, the total number of students in the senior class is:
Total_Senior = 7y + 3y = 10y
Setting Up the Equations
1. Difference in Total Students:
Given that there are 300 more students in the senior class than in the junior class:
10y = 5x + 300
(Equation 1)
2. Combined Ratio of Boys to Girls:
The combined ratio of boys to girls in both classes is given as 8 to 17:
(2x + 3y) / (3x + 7y) = 8 / 17
Cross-multiplying gives:
17(2x + 3y) = 8(3x + 7y)
This simplifies to:
34x + 51y = 24x + 56y
10x = 5y
Therefore, y = 2x
(Equation 2)
Substituting Equations
Now, substitute Equation 2 into Equation 1:
- Replacing y in Equation 1:
10(2x) = 5x + 300
20x = 5x + 300
15x = 300
x = 20
Now, substituting x back to find y:
- y = 2(20) = 40
Calculating Total Students in Senior Class
Now, calculate the number of students in the senior class:
Total_Senior = 10y = 10(40) = 400
Thus, the number of students in the senior class is 400.
The correct answer is option D.
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The ratio of boys to girls in the junior class is 2 to 3 respectively and the ratio of girls to boys in the senior class is 7 to 3 respectively. If there are 300 more students in the senior class than in the junior class and the combined ratio of boys to girls in both classes is 8 to 17 respectively, how many students are in the senior class?a)100b)300c)375d)400e)500Correct answer is option 'D'. Can you explain this answer?
Question Description
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