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