In a class of 80 seniors, there are 3 boys for every 5 girls. In the junior class, there are 3 boys for every 2 girls. If the two classes combined have an equal number of boys and girls, how many students are in the junior class?
If there are
3x senior boys and 5x senior girls
3y junior boys and 2y junior girls
3x+3y = 5x+2y
3x+5x = 80
so, x=10
and y=20
juniors have 60 boys and 40 girls.
seniors have 30 boys and 50 girls
3+5=8
80/8=10
x=10 YES
b=30 YES
g=50 YES
y=10 NO
b=30 NO
g=20 NO
Because 60 doesn't = 70
y=20 YES
b=60 YES
g=40 YES
Because 90 = 90
S = 30 boys and 50 girls
J = 60 boys and 50 girls
To solve this problem, we need to set up equations based on the given information and then solve for the unknown.
Let's suppose the number of boys in the senior class is B1, the number of girls in the senior class is G1, the number of boys in the junior class is B2, and the number of girls in the junior class is G2.
From the given information, we can establish the following equations:
Equation 1: B1 = (3/8) * (B1 + G1) => Simplifying, we get B1 = (3/5)G1
Equation 2: B2 = (3/5) * (B2 + G2)
Equation 3: G1 = (5/8) * 80 => Simplifying, we get G1 = 50
Equation 4: B1 + G1 = B2 + G2
Let's use substitution to solve the equations:
From Equation 1, we can substitute G1 = 50:
B1 = (3/5) * 50 => B1 = 30
From Equation 4, we can substitute B1 = 30:
30 + 50 = B2 + G2 => B2 + G2 = 80
Now, let's use the ratio between boys and girls in the junior class to solve Equation 2:
B2 = (3/2) * G2
Substituting this into Equation 4, we get:
(3/2)G2 + G2 = 80 => (5/2)G2 = 80 => G2 = (2/5) * 80 => G2 = 32
Finally, to find the total number of students in the junior class, we add the number of boys and girls:
B2 + G2 = (3/2)G2 + G2 = (3/2) * 32 + 32 = 48 + 32 = 80
Thus, there are 80 students in the junior class.