SOLUTION: 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

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Question 34418: 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.
Found 2 solutions by stanbon, lyra:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of students in the class be "x".
Number of boys is 0.60x
Number of girls is 0.40x
Later when the 6 boys are added you have
Number of boys is 0.60x+6
Number of girls is 0.40x-6
So the number of students overall has not changed.
Therefore the following equation applies:
EQUATION:
original # of boys + 6 = 75% of the class
0.60x + 6 = 0.75x
6= 0.15x
x= 40 (Number of students in the class)
0.6x=24 (original number of boys)
0.4x=16 (original number of girls)
Cheers,
Stan H.

Answer by lyra(94) About Me  (Show Source):
You can put this solution on YOUR website!
Alright, so we want to write the "words" as "math".
.6x%2Bg=x
.75x%2Bg=x
.6x%2B%28g-6%29=.75x%2Bg
.6x-.6x%2B%28g-6%29=.75x-.6x%2Bg
g-6=.15x%2Bg
100%28g-6%29=100%28.15x%2Bg%29
100g-600=15x%2B100g
100g-600-100g=15x%2B100g-100g
-600=15x
-600%2F15=15x%2F15
-40=x
See also,
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=-40.
  • Graphical form: Equation .6x%2B%28g-6%29=.75x%2Bg was fully solved.
  • Text form: .6x+(g-6)=.75x+g simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+.6x%2B%28g-6%29=.75x%2Bg+%29
    For tutors: simplify_cartoon( .6x+(g-6)=.75x+g )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .6%2Ax%2Bhighlight_red%28+%28g-6%29+%29=.75x%2Bg.
Remove unneeded parentheses around terms highlight_red%28+g+%29,highlight_red%28+-6+%29
It becomes .6%2Ax%2Bhighlight_green%28+g+%29-highlight_green%28+6+%29=.75x%2Bg.
Look at .6%2Ax%2Bg-6=highlight_red%28+.75%2Ax%2Bg+%29.
Moved these terms to the left highlight_green%28+-.75%2Ax+%29,highlight_green%28+-g+%29
It becomes .6%2Ax%2Bg-6-highlight_green%28+.75%2Ax+%29-highlight_green%28+g+%29=0.
Look at .6%2Ax%2Bg-highlight_red%28+6+%29-.75%2Ax-g=0.
Moved -6 to the right of expression
It becomes .6%2Ax%2Bg-.75%2Ax-g-highlight_green%28+6+%29=0.
Look at highlight_red%28+.6%2Ax+%29%2Bg-highlight_red%28+.75%2Ax+%29-g-6=0.
Eliminated similar terms highlight_red%28+.6%2Ax+%29,highlight_red%28+-.75%2Ax+%29 replacing them with highlight_green%28+%28.6-.75%29%2Ax+%29
It becomes highlight_green%28+%28.6-.75%29%2Ax+%29%2Bg-g-6=0.
Look at %28.6-.75%29%2Ax%2Bhighlight_red%28+g+%29-highlight_red%28+g+%29-6=0.
Eliminated similar terms highlight_red%28+g+%29,highlight_red%28+-g+%29 replacing them with highlight_green%28+%281-1%29%2Ag+%29
It becomes %28.6-.75%29%2Ax%2Bhighlight_green%28+%281-1%29%2Ag+%29-6=0.
Look at %28highlight_red%28+.6+%29-highlight_red%28+.75+%29%29%2Ax%2B%281-1%29%2Ag-6=0.
Replace constants in expression: highlight_red%28+.6+%29,highlight_red%28+-.75+%29 with highlight_green%28+-0.15+%29
It becomes %28highlight_green%28+-0.15+%29%29%2Ax%2B%281-1%29%2Ag-6=0.
Look at %28-0.15%29%2Ax%2Bhighlight_red%28+%281-1%29%2Ag+%29-6=0.
Since highlight_red%28+%281-1%29%2Ag+%29 has zero as a factor, it should be replaced with a zero
Look at %28-0.15%29%2Ax%2B0-6=0.
Added fractions or integers together
It becomes %28-0.15%29%2Ax%2B0-6=0.
Look at %28-0.15%29%2Ax%2Bhighlight_red%28+0+%29-6=0.
Remove extraneous zero highlight_red%28+0+%29
It becomes %28-0.15%29%2Ax-6=0.
Look at %28highlight_red%28+-0.15+%29%29%2Ax-6=0.
Removed extra sign in front of -0.15
It becomes %28-highlight_green%28+0.15+%29%29%2Ax-6=0.
Look at highlight_red%28+%28-highlight_red%28+0.15+%29%29%2Ax+%29-6=0.
Remove unneeded parentheses around factor highlight_red%28+0.15+%29
It becomes -highlight_green%28+0.15+%29%2Ax-6=0.
Look at highlight_red%28+-0.15%2Ax-6+%29=0.
Solved linear equation highlight_red%28+-0.15%2Ax-6=0+%29 equivalent to -0.15*x-6 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=-40.

Universal Simplifier and Solver


Done!

Since there can't be a negative amount of people, we remove the negative sign getting:
x=40
Now we plug this into the original equation:
.6%2840%29%2Bg=40
24%2Bg=40 So there are 24 boys in the class.
24-24%2Bg=40-24
g=16 There are 16 girls in the class.
So the answer is that on the first day of class there were 16 girls and 24 boys.
We can check that our answer works:
.6%2A40=24 That works
.4%2A40=16 That works
16-6=10
24%2B6=30
.75%2A40=30 That works
.25%2A40=10 That works
Yep, everything checks, we have the right answer.
Hope this helps,
lyra