Percentage Problems

# Percentage Of

1.      In Chicago in the year 2000, there were approximately 1.053 million African Americans, 907 thousand whites (non-Hispanic), and 754 thousand Hispanics, and 181 thousand others (other races or two or more races).  What percent of Chicagoans in 2000 were of Hispanic origin?

Solution:

% of Hispanics = # of Hispanics / Total Population

% of Hispanics = 754,000 / (1,053,000 + 907,000 + 754,000 + 181,000)

% of Hispanics = 0.26 * 100%

% of Hispanics = 26%

2.      54% of DePauls student body of approximately 21,000 is female.  Approximate how many females attend DePaul?

Solution:

% of female students = # of female students / 21,000

# of female students = % of female students * 21,000

# of female students = 54% of female students * 21,000

# of female students = 0.54 * 21,000

# of female students = 11,340

3.      Chicagos population grew from 2.78 million in 1990 to 2.90 million in 2000.  By how many percent did it grow?

Solution:

Percentage Change = (new  old ) / old

Percentage Change = (2.90  2.78) / 2.78

Percentage Change = 0.0432

Percentage Change = 0.0432 * 100%

Percentage Change = 4.32%

4.      In 1996, 94,007 tons of waste was recycled in Chicagos blue bag recycling program. In the year 2000, 296,363 tons were recycled.  By how many percent did it increase from 1996 to 2000?

Solution:

Percentage Change = (296,363 tons  94,007 tons) / 94,007 tons

Percentage Change = 202,356 / 94,007

Percentage Change = 2.15 * 100%

Percentage Change =  215%

# Percent More Than; Times More Than

5.      The life expectancy in Canada is 79.1 years; the life expectancy in the US is 76.0 years. By how many percent is the life expectancy of Canada higher than the life expectancy in the US?

Solution:

The key word for this kind of problems is "than". Whatever is after "than" should go in the denominator (bottom part).

How many percent more = (Canada  US) / US

How many percent more = (79.1  76) / 76

How many percent more = 3.1 / 76

How many percent more = 0.0407 * 100%

How many percent more = 4.07%

6.      By how many percent is the life expectancy of people in the US lower than the life expectancy in Canada?

Solution:

How many percent less = (76  79.1) / 79.1

How many percent less = 3.1 / 79.1

How many percent less = 0.0392 * 100%

How many percent less = 3.92%

7.      How many times more is the life expectancy of Canada higher than the life expectancy in the US?

Solution:

We expect a number here!

How many times more = Canada / US

How many times more = 79.1 / 76

How many times more = 1.041

# Successive Percentage Change

8.      Spot prices for crude oil are rather volatile.  From 1998 to 1999, spot prices for crude oil decreased by 28%.  From 1999 to 2000, they increased by 106%.  What was the percentage change over the two year period from 1998 to 2000?

Solution:

A short way to do this kind of problem is

Percentage change over two year period = (1 ± %)(1 ± %)  1

Percentage change over two year period = (1  28%)(1 + 106%)  1

Percentage change over two year period = (1  0.28)(1 + 1.06)  1

Percentage change over two year period = (0.72)(2.06%)  1

Percentage change over two year period = 1.4832  1

Percentage change over two year period = 0.4832 * 100%

Percentage change over two year period = 48.32%

An increase of 48.32% over the original price!

9.  Suppose you are earning a salary of \$1,000 per week. Your company experiences a slowdown in earnings, and asks all workers to take a 20% pay cut. What is your salary after the cut? Six months later, the company recovers and it offers you a 20% increase on your current salary. How much will you be earning after the increase?

Solution:

New salary = (1  20%)(1 + 20%)  1

New salary = (1  0.20)(1 + 0.20)  1

New salary = (0.80)(1.20)  1

New salary = 0.96  1

New salary = 0.04 * 100%

New salary will have a decrease of 4%, or (\$1000  \$1000 * 0.04) = \$960

10. According to the official 2000 census, the Hispanic population of the US in 2000 was 35,305,818. It rose by an astounding 57.9% from 1990 to 2000.  What was the Hispanic population in 1990?

Solution:

1990    →        2000

old                  new

old                  35,305,818

If we use the percentage change formula, then

% change = (new  old) / old

57.9% = (35,305,818  old) / old

doing some algebra

0.579 * old = 35,305,818  old

0.579 * old + old = 35,305,818

1.579 * old = 35,305,818

old = 35,305,818 / 1.579

old = 22,359,606

11. From a news article: "In the first six months of 1996, the number of deaths [from AIDS] fell 12% to 22,000 [compared to the same period a year earlier]." How many AIDS deaths were there during the first six months of 1995?

Solution:

1995    →        1996

old                  new

old                  22,000

Because there was a 12% decrease, we have to use 12%

12% = (22,000  old) / old

0.12 * old = 22,000  old

0.12 * old + old = 22,000

0.88 * old = 22,000

old = 22,000 / 0.88

old = 25,000