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

Algebra.Com
Question 34457: 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.
Answer by lyra(94)   (Show Source): You can put this solution on YOUR website!
Alright, so we want to write the "words" as "math".











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 was fully solved.
  • Text form: .6x+(g-6)=.75x+g simplifies to 0=0
  • Cartoon (animation) form:
    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 .
Remove unneeded parentheses around terms highlight_red%28+g+%29,highlight_red%28+-6+%29
It becomes .
Look at .
Moved these terms to the left highlight_green%28+-.75%2Ax+%29,highlight_green%28+-g+%29
It becomes .
Look at .
Moved -6 to the right of expression
It becomes .
Look at .
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 .
Look at .
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 .
Look at .
Replace constants in expression: highlight_red%28+.6+%29,highlight_red%28+-.75+%29 with highlight_green%28+-0.15+%29
It becomes .
Look at .
Since highlight_red%28+%281-1%29%2Ag+%29 has zero as a factor, it should be replaced with a zero
Look at .
Added fractions or integers together
It becomes .
Look at .
Remove extraneous zero highlight_red%28+0+%29
It becomes .
Look at .
Removed extra sign in front of -0.15
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+0.15+%29
It becomes .
Look at .
Solved linear equation highlight_red%28+-0.15%2Ax-6=0+%29 equivalent to -0.15*x-6 =0
It becomes .
Result:
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:

Now we plug this into the original equation:

So there are 24 boys in the class.

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:
That works
That works


That works
That works
Yep, everything checks, we have the right answer.
Hope this helps,
lyra
RELATED QUESTIONS

On the first day of school, the percentage of boys in a particular class is 60%. During... (answered by stanbon,mewtwo1,josmiceli)
On the first day of school, the percentage of boys in a particular class is 60%. During... (answered by checkley71)
On the first day of school, the percentage of boys in a particular class is 60%. During... (answered by stanbon,lyra)
On the first day of school, the percentage of boys in a particular class is 60%. During... (answered by stanbon)
On the first day of school, the percentage of boys in a particular class is 60%. During... (answered by checkley71)
How would I solve this : On the first day of school, the percentage of boys in a... (answered by ptaylor)
On the first day of school, the percentage of boys in a particular class is 60%. During... (answered by mangopeeler07)
On the first day of school, the percentage of boys in a particular class is 60%. During... (answered by Mathtut)
On the first day of school, the percentage of boys in a particular class is 60%. During... (answered by anantha)