Math 2000 Midterm Exam Solutions

Spring 2002

Distribution: 90-100: 9; 80-89: 11; 70-79: 9; 60-69:11; <60: 7.

1a. We can do a unit conversion from deaths per year to deaths per minute:

There are about 4.4 deaths per minute in this country.

1b. The fraction of deaths due to hearth disease is

About 32% of all deaths are due to heart disease.

1c. We can start by finding the number of accident deaths per person in this country. Remembering that the U.S. population is 280 million, the number of deaths per person is

If we now count deaths per every 100,000 people, the death rate is 0.00035 × 100,000 = 35 deaths per 100,000 people.

2a. Because 1 euro = $0.95, 1 euro is worth less than $1; that is, $1 is larger than 1 euro.

2b. Because 1 pound = $1.60, we can write the conversion factor as

Doing the division in the second expression, we have

We see that there are about 0.625 pounds per dollar.

2c. We must do the unit conversion from pounds (English) per kilogram to dollars per pound, using the conversion factors 1 kg = 2.2 lbs and 1 pound (English) = $1.60.

The price is $0.91 per pound.

3a. The sentence that describes this situation is

3.2% of all eligible workers = 8.9 million people.

Rewriting this sentence, we have

0.032 × eligible workers = 8.9 million people.

Dividing both sides by 0.032, we see that

(Something is wrong with this quote because the number of eligible workers is almost the entire U.S. population.)

3b. The sentence that describes the situation is

Sept spending + (2.9% of Sept spending) = Jan spending = $7.2 million.

Rewriting this sentence, we have

(100% of Sept spending) + (2.9% of Sept spending) = $7.2 million

or

(102.9% of Sept spending) = $7.2 million.

Noting that 102.9% = 1.029, and dividing by 1.029, we see that

Consumer spending in September was $7.0 trillion.

4a. Using the savings plan formula with PMT = $200, APR = 9.8% = 0.098, Y = 25 years, and n = 12, we see that the accumulated balance after 25 years is

4b. Robert makes 300 payments of $200, which means he deposits $200 × 300 = $60,000 of his own money. The remaining balance, which is $256,497 - $60,000 = $196,497, is due to interest. Therefore the fraction of the balance due to interest is

About 77% of the total balance is due to interest.

5a. Several diagrams would work. Here are three of them:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


The first diagram has the disadvantage that it suggest that there are doctors and nurses who are neither men nor women. The second and third diagrams avoid this possibility.

6a. We see that $618,000 million = $6.18 × 105 million. Noting that 1 million = 106, we have

$618,000 million = $6.18 × 105 million = $6.18 × 105 × 106 = $6.18 × 1011.

6b. We are told that 44% of the total population of 280 million is under age 24. Thus,

44% × 280 million = 123 million people = 1.23 × 108 people.

are under age 24.

6c. Total spending per person under age 24 is

About $5000 is spent on education per person under age 24.