SOLUTION: The ratio of the number if boys and girls in a school is 3: 2. 20% of the boys and 25% of the girls are scholarship holders. The percentage of the school students who are no

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The ratio of the number if boys and girls in a school is 3: 2. 20% of the boys and 25% of the girls are scholarship holders. The percentage of the school students who are no      Log On


   

Question 978652: The ratio of the number if boys and girls in a school is 3: 2. 20% of the
boys and 25% of the girls are scholarship holders. The percentage of the
school students who are not scholarship holders is:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The ratio of the number if boys and girls in a school is 3:2
To change a ratio to two fractions, put each number, 3 and 2, over the sum of
the two numbers 3+2, or 5. So the two fractions are 3%2F5 and 2%2F5.

That means 3%2F5ths of the students are boys and 2%2F5ths of the students are
girls.

Change those to percents:

3%2F5=60%2F100=%2260%25%22, 2%2F5=40%2F100=%2240%25%22

So 60% of the students are boys and 40% of the students are girls.

20% of the boys and 25% of the girls are scholarship holders
That means 20% of 60% are boy scholarship holders and 25% of 40% are girl scholarship holders.

Therefore:

20% of 60% = (0.20)(0.60) = 0.12 = 12% of the students are boy scholarship
holders, 

and

25% of 40% = (0.25)(0.40) = 0.10 = 10% of the students are girl scholarship
holders. 

That means that 12% + 10% = 22% of the students are scholarship holders.

Therefore 100% - 22% = 78% of the students are not scholarship holders.

Edwin