WHAT PERCENT?
THE METHOD OF PROPORTIONS

PROBLEMS

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11.  28 out of 100 students got A.

11.  a)  What percent got A?  28%

11.  b)  What percent did not get A?  72%

12.  81 students in the class were brunettes, 14 were blondes, and 5 were
12.  red-heads.  

12.  a)  What percent were brunettes?  81%, since 81 + 14 + 5 = 100.

12.  b)  What percent were blondes?  14%

12.  c)  What percent were red-heads?  5%

13.  a)  32 out of 100 people responded Yes.  What percent responded
13.  a)  Yes?  32%

13.  b)  32 out of 200 people responded Yes.  What percent responded
13.  b)  Yes?  16%

13.  c)  32 out of 50 people responded Yes.  What percent responded
13.  c)  Yes?  64%

14.  Solve each proportion. And explain why each one is a proportion.

14.   a)  9 out of 20  is equal to  45 out of 100.  Because:

5 times 20 is 100. And 5 times 9 is 45.

14.  a)  9 is what percent of 20?  45%

14.   b)  27 out of 300  is equal to  9 out of 100.  Because:

A third of 300 is 100. And a third of 27 is 9.

14.  a)  27 is what percent of 300?  9%

14.   c)  8 out of 32  is equal to  25 out of 100.  Because:

8 is a quarter of 32. And 25 is a quarter of 100.

14.  a)  8 is what percent of 32?  25%

15.  In a class of 25 students, 4 were absent.  What percent were
16.  absent?  16%

16.  What percent were present?  84%

16.  Jennifer had $50 and she spent $49.  What percent of her money did
17.  she spend?  98%

17.  What percent does she have left?  2%

17.  A team played 20 games and won 17 of them.  What percent did
18.  they win?  85%

17.  What percent did they lose?  15%

18.  In a survey of 200 people, 84 responded Yes.  What percent
18.  responded Yes?  42%

19.  In a survey of 200 people, 85 responded Yes.  What percent
19.  responded Yes?  42½%

10.  128 out of 400 students took French.  What percent took
10.  French?  32%

11.  129 out of 400 students took French.  What percent took
11.  French?  32¼%

12.  In a survey of 1000 students, 682 responded No.  What percent
14.  responded No?  68.2%.  What percent responded Yes?  31.8%

13.  In a later survey of 1000 students, 846 responded No.  What percent
15.  responded No?  84.6%  What percent responded Yes?  15.4%

14.  500 people recently voted, and 325 voted for candidate A.  What
12.  percent voted for candidate A?  65%.  What percent did not vote for
12.  candidate A?  35%

(Compare Example 9.)

15.  500 people recently voted, and 328 voted for candidate B.  What
13.  percent voted for candidate A?  34.4%.  What percent did not vote
13.  for candidate A?  65.6%

16.  In each of the following, the Amount has what ratio to -- is what
16.  percent of -- the Base?

16.  For example, 15 is what percent of 20?

15 is three fourths of 20

16.  because 15 and 20 have a common divisor 5.  Therefore,

15 is 75% of 20.

16.  a)  9 is what percent of 45?

9 is the fifth part of 45. 9 is 20% of 45.

16.  b)  What percent of 16 is 4?

4 is the fourth part of 16. 4 is 25% of 16.

16.  c)  What percent of 4 is 16?

16 is four times 4. 16 is 400% of 4.

16.  d)  12 is what percent of 36?

  12 is the third part of 36. 12 is 33 1
3
% of 36.

16.  e)  What percent of 18 is 9?

9 is half of 18. 9 is 50% of 18.

16.  f)  What percent of 9 is 18?

18 is two times of 9. 18 is 200% of 9.

16.  g)  6 is what percent of 60?

6 is the tenth part of 60. 6 is 10% of 60.

16.  h)  18 is what percent of 60?

18 is the three tenths of 60. 18 is 30% of 60.

16.  i)  12 is what percent of 30?

12 is the two fifths of 30. (Common divisor 6.) 12 is 40% of 30.

16.  j)  18 is what percent of 27?

  18 is two thirds of 27. 18 is 66 2
3
% of 27.

16.  k)  7 is what percent of 56?

7 is the eighth part of 56. 7 is 12½% of 56.

16.  l)  20 is what percent of 8?

20 is two and a half times 8. 20 is 250% of 8.

16.  m)  What percent of 4 is 13?

13 is three and a quarter times 4. 13 is 325% of 4.

17.  Clearing of decimals.  Rephrase each question with whole
17.  numbers. Then answer it.

  a)   1.5 is what percent of 2?  15 is what percent of 20?  75%.
 
  b)   .2 is what percent of 5?  2 is what percent of 50?  4%.
 
  c)   2 is what percent of 2.5?   20 is what percent of 25?  80%.
 
  d)   What percent of 5 is 7.5?  75 is what percent of 50?  150%.
 
  e)   What percent of 2 is 2.5?   25 is what percent of 20?  125%.
 
  f)   What percent of 4 is .5?  5 is what percent of 40?  12.5%.

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