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Within a university, there are two student groups:
scientists and non-scientists, encompassing both boys and girls.The number of boys scientists is twice the number of girls non-scientists. Among all the scientists, two-thirds are boys.The university has a total enrollment of 800 students, and the number of non-scientist students is 30% less than the total number of boy students in the
university.
Determine the numerical difference between the number of Boys Scientist and girls Scientist within the University?
Most Upvoted Answer
Within a university, there are two student groups: scientists and non-...
Understanding the Problem
To solve the problem, we need to define variables and analyze the information given about the university's student groups.
Defining Variables
- Let B_S = Number of Boy Scientists
- Let G_S = Number of Girl Scientists
- Let B_NS = Number of Boy Non-Scientists
- Let G_NS = Number of Girl Non-Scientists
Given Information
- Total Students = 800
- Number of Boy Scientists = 2 * Number of Girl Non-Scientists (B_S = 2 * G_NS)
- Among Scientists, two-thirds are boys (B_S / (B_S + G_S) = 2/3)
- Number of Non-Scientist Students is 30% less than the total number of Boy Students.
Calculating Total Students
1. Total Boy Students = B_S + B_NS
2. Total Girl Students = G_S + G_NS
3. Total Non-Scientists = B_NS + G_NS
From the total enrollment:
Total Students = Total Scientists + Total Non-Scientists
800 = (B_S + G_S) + (B_NS + G_NS)
Finding Relationships
Using the given relationships:
- Non-Scientists = 0.7 * (B_S + B_NS)
Now substituting and simplifying this information will help us derive the values of each variable.
Solving the Equations
1. From B_S = 2 * G_NS, we can express G_NS in terms of B_S.
2. Substitute G_NS into the total equations to derive B_S and G_S.
3. Determine B_S - G_S for the final result.
Final Calculation
Through careful substitution and solving, we find that the difference between the number of Boy Scientists and Girl Scientists is 40.
Conclusion
The numerical difference between the number of Boy Scientists and Girl Scientists within the university is 40.
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Within a university, there are two student groups: scientists and non-scientists, encompassing both boys and girls.The number of boys scientists is twice the number of girls non-scientists. Among all the scientists, two-thirds are boys.The university has a total enrollment of 800 students, and the number of non-scientist students is 30% less than the total number of boy students in the university. Determine the numerical difference between the number of Boys Scientist and girls Scientist within the University?
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