Question 339182: I need to find the system of linear equations. It has to be two equations with two variables each.
On the first day of school, the percentage of boys in a particular class is 60%. During the school year, six girls move away, and are replaced in the class by six boys. This makes the class roster 75% boys. Find the number of boys and girls in the class on the first day of school.
The teacher has given this as a hint:
1. Let x = # of boys on the first day. Let y = # of girls on the first day.
2. Answer the question: In terms of x and y, how many boys and girls total on the first day?
3. Answer the question: Using the answer to # 2, what is 60% of this total.
4. The given info says x = answer to # 3.
That will give you your first equation.
For the second equation
5. How do you increase x (the # of boys) by 6?
6. Repeat #2 and #3 but with 75%.
7. Set your answer from # 6 equal to your answer to #5.
I know how many boys and girls there were, but even with the hint, I cannot figure out what the equations are supposed to be.
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! let boys be x
girls be y
..
total students = x+y
..
60 % are boys
..
Number of boys = 0.6(x+y)
Number of girls = 0.4(x+y)
..
When you add 6 boys to the class
The number of boys = 0.6(x+y)+6
..
The total remains the same.(x+y)
The boys increases to 75% of total = 0.75(x+y)
..
0.6(x+y)+6=0.75(x+y)
0.6x+0.6y+6 = 0.75x+0.75y
add -0.6x and -0.6y to both sides
0.6x-0.6x+0.6y-0.6y+6 = 0.75x+0.75y-0.6x-0.6y
6 = 0.15x+0.15y
6=0.15(x+y)
divide by 0.15
6/0.15 = 0.15/0.15 * (x+y)
x+y= 40
..
on the first day 60% were boys
60% of 40 are boys
0.6 * 40 = 24 boys.
..
the balance 16 were girls on the first day.
..
CHECK
add 6 +24 = 30
30/40 = 3/4 = 75%
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