Question 29466: This is confusing me. Maybe it is the percents in the problem. We are encouraged to use substitution or elimination to solve this. I tried to set it up...but I am so confused. Here is the problem:
On the first day of school, the percentage of boys in a class is 60%. In the middle of the year 6 girls move away and are replaced by 6 boys. This makes the roster now 75% boys. Find the number of boys and girls in the class on the first day of school.
Thanks for your help!
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! This is confusing me. Maybe it is the percents in the problem. We are encouraged to use substitution or elimination to solve this. I tried to set it up...but I am so confused. Here is the problem:
On the first day of school, the percentage of boys in a class is 60%. In the middle of the year 6 girls move away and are replaced by 6 boys. This makes the roster now 75% boys. Find the number of boys and girls in the class on the first day of school.
Thanks for your help!
DONT DESPAIR..YOU WERE DOING FINE EARLIER...GO ABOUT THE SAME WAY..
LET THE TOTAL STRENGTH BE 100X....YOU CAN TAKE X ALSO ..BUT IN % SUMS IT WILL ELIMINATE DECIMALS/FRACTIONS IF WE USE 100X....OK...
I DAY......BOYS ARE 60%..OF TOTAL =100X*60/100=60X
HENCE GIRLS ARE
100X-60X=40X
MID YEAR...6 GIRLS ARE REPLACED BY 6 BOYS...(WHY?...BOYS ARE BETTER BEHAVED?)!!!
SO WE HAVE BOYS =60X+6
AND GIRLS =40X-6
TOTAL = 60X+6+40X-6=100X
SO % BOYS NOW =100*(60X+6)/100X=(60X+6)/X
THIS IS 75...SO...
(60X+6)/X=75
6OX+6=75X
75X-60X=6
15X=6
X=6/15=2/5
SO TOTAL STRENGTH ON I DAY =100*2/5=40
BOYS ARE 40*60/100=24...
AND GIRLS ARE 40-24 = 16......
GOT IT ..TRY DOING WITH X AS STRENGTH...AND YOU WILL GET THE SAME ANSWER...X=40
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