SOLUTION: I need help with an algebra word problem with system of equations.
on the first day of school, 60% of the class were boys. During the school year six girls moved away and 6 boys
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Question 199118: I need help with an algebra word problem with system of equations.
on the first day of school, 60% of the class were boys. During the school year six girls moved away and 6 boys replaced them. At the end of the year, 75% of the class were boys. What is the number of boys and girls on the first day?
I've tried to do this:
60% of (x + y) = x
40% of (x + y) = y
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x=# of boys and y=# of girls
Since there's only a choice between boys or girls, this means that there is a total of students. Also, because "on the first day of school, 60% of the class were boys", this means that (ie take 60% of the total and you get "x")
Also, since "During the school year six girls moved away and 6 boys replaced them." and "At the end of the year, 75% of the class were boys", we know that where "x+6" is the new count for the boys and "y-6" is the new count for the girls.
----------------------------------------
Start with the first equation.
Distribute
Multiply EVERY term by 10 to make every number a whole number.
Multiply
Subtract 10x from both sides.
Combine like terms. So this is the new equation #1.
----------------------------------------
Start with the second equation.
Remove the inner parenthesis.
Combine like terms.
Distribute
Multiply EVERY term by 100 to make every number a whole number.
Multiply.
Subtract 100x from both sides.
Combine like terms. So this the new equation #2.
So we have the system of equations:
Let's solve this system by use of substitution.
In order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.
So let's isolate y in the first equation
Start with the first equation
Add to both sides
Divide both sides by
Reduce
---------------------
Since , we can now replace each in the second equation with to solve for
Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.
Multiply.
Multiply EVERY term by the LCD 3. This will eliminate the fractions.
Multiply.
Combine like terms on the left side
Divide both sides by 75 to isolate x
Divide
-----------------First Answer------------------------------
So the first part of our answer is: .
This means that there are 24 boys (at the beginning of the school year)
Since we know that we can plug it into the equation (remember we previously solved for in the first equation).
Start with the equation where was previously isolated.
Plug in
Multiply
Reduce.
-----------------Second Answer------------------------------
So the second part of our answer is: This means that there are 16 girls (at the beginning of the school year)
===================================================================
Summary:
So our answers are: and
This means that at the beginning of the school year, there are 24 boys and 16 girls. At the end of the school year, there are 30 boys and 10 girls.
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