Determining the Number of Boys in a Group of 27 Students

Q)
In a group of 27 students every girl knows four boys and every boy knows five girls. Find the number of boys in the group.

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A)
To solve this problem, let's denote the number of boys in the group as B and the number of girls as G. We know that the total number of students in the group is 27, so we can express the relationship between the number of boys and girls as:

G+B=27

We also know that each girl knows four boys and each boy knows five girls. This information can be used to express the total number of known pairs between boys and girls. The total number of such pairs from the girls' perspective is 4G (since each of the G girls knows 4 boys), and from the boys' perspective, it is 5B (since each of the B boys knows 5 girls).

Since these pairs are the same, we can set these two expressions equal to each other:

4G=5B

Now we have two equations:

1. G+B=27
2. 4G=5B

We can solve this system of equations to find the values of G and B. Let's solve for B, the number of boys in the group.

4(27-B)=5B
108=9B
B=12

The number of boys in the group of 27 students, where every girl knows four boys and every boy knows five girls, is 12.

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from sympy import symbols, Eq, solve

# Defining the symbols
G, B = symbols('G B')

# Defining the equations
equation1 = Eq(G + B, 27)
equation2 = Eq(4*G, 5*B)

# Solving the system of equations
solution = solve((equation1, equation2), (G, B))
number_of_boys = solution[B]
number_of_boys

1. Defining Symbols: The symbols G and B are defined using sympy.symbols. They represent the number of girls and boys, respectively.
2. Creating Equations: Two equations are defined using Eq.
   • equation1 = Eq(G + B, 27) represents the total number of students (27), which is the sum of the number of girls (G) and boys (B).
   • equation2 = Eq(4*G, 5*B) represents the relationship between the number of connections each girl and boy has (each girl knows 4 boys, and each boy knows 5 girls).
3. Solving the Equations: solve((equation1, equation2), (G, B)) solves the system of equations for G and B. The solve function returns a dictionary where keys are the symbols (G and B) and values are their corresponding solutions.
4. Accessing the Solution for B: solution[B] accesses the value of B in the solution dictionary. In this context, solution is a dictionary with keys G and B. By using solution[B], you retrieve the solution for the number of boys in the group.

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