Homework 3
Math 114Q, Section 10

Due in class Tuesday, September 25; Remember to show work and write in full sentences.

  1. On September 20 NPR's Morning Edition reported that there are 47 milliion Americans without health insurance. In the same piece the reporter quoted Governor Schwarzenegger of California saying that his state had 4.7 million uninsured residents.

    Compare the percentage of the population without medical insurance in California with the percentage for the Unites States as a whole.

  2. In the September 20 Boston Globe columnist Joan Vennochi wrote about Reading, writing, and cheating. (That's a link to the text of her oped piece.)

    1. In her essay Vennochi reports on the percentage of students who admit to having cheated on a test, and on the percentage who agree that "In the real world, successful people do what they must to win, even if others consider it cheating." First, find the reported percentages. From this information you cannot figure out how many students both cheated and agreed with the statement, but you can figure out the smallest and largest possible percentages for the overlap. Do that, explaining your thinking.

    2. Find out as much as you can about the source of the statistics Vennochi quotes.

  3. In the September 20 Boston Globe columnist Steven Syre wrote a column entitled "No happy ending yet." Here's a link to the text. In that column he reports on the number and percentage of empty houses in America.

    1. Use the information he provides to calculate how many houses there are in America.

    2. Bonus. Suppose that on average four people live in each occupied house. Estimate the percentage of the population of the United States who live in houses.

  4. Currency conversion. When you read this question you will see that you need at least two days to answer it. So if you come to it for the first time the day the assignment is due, you may be in trouble.

    1. Suppose your company is sending you to France for business, and asks you to convert $1250 (U.S. dollars) to Euros in preparation for your trip. Find a currency conversion calculator on the web and use it to tell you how many Euros your $1250 will buy. Your answer should identify the web site, the date and time and the conversion factor used (in Euros/dollar) as well as the amount of Euros you would get.

    2. The next day (or some days later) they call off the trip. Go back to the web to figure out what you would get back in dollars for the Euros you bought a day or so ago for $1250. Again identify the web site, date and time, and conversion factor, this time in dollars/Euro. What percentage gain (or loss) did you incur due to the change in exchange rate?

    3. If you actually converted dollars to Euros and back the bank would charge a fee each time. Suppose that fee is 2% of the amount converted. Figure out how many Euros you would have gotten in the first conversion, then how many dollars back in the second, then your percentage gain (or loss).

    4. If the conversion rate was exactly the same each time (unlikely, but imagine it) would your loss in the conversion to Euros and back be 4%? Explain your answer, don't just say "yes" or "no".

  5. Here's part of a problem from last year's Math 114 final exam: If the United States converted to the metric system we would have to replace all our speed limit signs. What would this one look like if miles per hour were converted to kilometers per hour? (Look up the conversion factor for turning miles into kilometers.)

  6. I read somewhere on the web that Google serves 100 billion web searches per year. Is this number reasonable?

    Note: We're not asking if this number is correct, just if it's reasonable. "I think so" or "I think not" isn't a satisfactory answer. And you can't answer this question by looking up the right number on the web to see if it's about 100 billion. Then you'd just be quoting one web site to argue with (or support) the claim on this one.

  7. Suppose you drive from Here to There at 30 miles/hour and then the same route back from There to Here at 60 miles/hour. What is your average speed for the round trip? (Warning: you need to figure this out. It's not 45 miles/hour!)

  8. Unit conversion

  9. The answers to hw2 are posted at www.cs.umb.edu/~eb/m114/hw2/hw2Answers.html. Look at them, and read the comments on your graded paper. If there are things you still don't understand, be prepared to ask. If you want to practice, try doing some of the problems over again (in your own words, not ours). You can resubmit them and we will read them again.

  10. In the answers to hw2 you can discover there that between last year and this the percentage of 10th graders in the Boston public schools who failed the Math MCAS test fell by 3 percentage points from 12% to 9%. Here's a question based on that information.

    How many 10th graders in Boston failed the Math MCAS in 2007?

    You may be able to find the exact answer on the web. (We haven't looked and don't know). If you can, do. But whether or not you can, figure it out this way: use the web to find out something about the population of Boston, or the school population, and then estimate how many of those are 10th graders.

    Be sure to document all your sources.

    Do you have enough information to determinte how many tenth graders failed this year?

  11. Bonus problem. Driving to school on September 18 I heard on NPR news that the Producer Price Index fell by 1.4 percent in August. The Producer Price Index does for wholesale prices what the Consumer Price Index does for retail transactions. The reporter said that surprising drop was a reflection of a 14% drop in gasoline prices. He also seemed to say that most other prices were about the same. (The NPR web site links to an Associated Press report with the first of these two numbers. I can't find the second there.)

    The PPI, like the CPI, is computed as an average price change for a mix of goods and services. Use the data above to figure out what fraction (or percent) of that mix is the contribution of gasoline prices.

    There are several ways to do this problem. Here is one way to start. Suppose the mix of goods and services was priced at $100 in July, and that gasoline costs contributed $G to that $100. G is what you need to find.

    Here are some questions you might want to answer on your way to a solution.

    Then you could combine these answers in an algebraic equation for G, and solve it. Or you could try guessing values for G, and checking each guess until you find a value that fits the facts.

    The important part of whatever method you choose is thinking clearly and writing down what you are thinking. Don't just throw together a bunch of numbers.

    If you succeed in finding a value for G, try to compare the value to one in the CPI mix table from the answer to hw2, or find the table for the PPI at the government's PPI web page www.bls.gov/ppi/.