Math 2000 - Solutions 4

Spring 2001

4c. Sentence: 15% of total = 150, or 0.15 × total = 150. Therefore, the total is 150/0.15 = 1000. You should check to see that this answer makes sense. If it is correct, it must follow that 15% of 1000 is really 150. Check that 0.15 ´ 1000 = 150, as required.

7c. We are told that defense spending decreased from $266 billion (previous value) to $254 billion (new value). The absolute change was $254 billion - $266 billion = -$12 billion. The percentage change was

Between 1995 and 1997 the U.S. defense budget changed by -4.5%, which is a decrease of 4.5%.

8c. The absolute change in the number of single-family households is 30% - 12% = 18 percentage points. This represents a relative change of 18/12 = 150%. The percentage of single-family households has increased by 150%.

10d. The words “than in the United States” tell us that the life expectancy in the United States is the reference quantity. The absolute difference is

79.1 yr - 76.0 yr = 3.1 yr.

To find the relative and percentage difference, we divide the absolute difference by the reference quantity:

The life expectancy in Canada is about 4% higher than in the United States.

16a. This statement expresses the percent difference between the populations of China and India. The absolute difference, with India as the reference quantity, is

1.20 billion - 0.95 billion = 0.25 billion.

Thus, China has

more people than India.

16b. This statement expresses the ratio of the populations of China and the United States. The ratio of the populations, with the United States as the reference quantity, is

Thus, China is a factor of 4.4 times more populous than the United States. We could say the population of China is 440% of the U.S. population or 340% more than the U.S. population.

24a. This statement is true. Imagine that there are 100 people in the class. Then 60 people are women and 6 of the women have blond hair. Thus 6% of the people are blond-haired women.

32b. If bagel sales increase by 20% each year, they will be 100% + 20% = 120% higher next year than this year. Thus

next year’s sales = 1.20 ´ this year’s sales

= 1.20 ´ $3 billion = $3.6 billion.