2.2.2: Exercise 2.2

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MAKING CONNECTIONS TO THE COLLABORATION

(1) Which of the following was one of the main mathematical ideas of the collaboration?

(i) There are two good places to buy watermelon: Byler’s and Kroger.

(ii) The cost of a bag of chips depends on how big it is.

(iii) All chips cost the same in terms of price per ounce.

(iv) The cost of chips per ounce represents a unit rate found by dividing the cost of the bag by the number of ounces it weighs.

DEVELOPING SKILLS AND UNDERSTANDING

(2) In this collaboration, you used ratios:

$\dfrac{cost\;of\;chips\;in\;dollars}{ounces\;of\;chips} = price\;of\;chips\;per\;ounce$

$\dfrac{weight\;of\;watermelon}{price\;of\;watermelon} = weight\;of\;watermelon\;per\;dollar$

Which of the following are ratios? There may be more than one correct answer.

(i) 252 miles

(ii) 67 hours

(iii) 10 miles/hour

(iv) 5 pounds/$3

(v) $98

(3) Calculate the gas mileage of a car that drives 283 miles on 12.3 gallons of gas. Round to the nearest mile per gallon.

(4) A car drives 630 miles on 35 gallons of gas. How far can it drive on 12 gallons?

(5) A jar holds 128 fluid ounces of juice. The label says the jar has 16 servings. How many fluid ounces are needed for 80 servings?

(6) According to the oil company BP, in 2021, the United States used 18,684,000 barrels of oil a day, and worldwide, people used around 94,088,000 barrels of oil per day.⁷ This includes oil used for (among other things) fuel and manufacturing.

(a) If there were 333 million people in the United States in 2021, what was the daily consumption rate per capita (barrels per person) in the United States? Round to the nearest hundredth of a barrel.

(b) If there were 7.89 billion people in the world in 2021, which of the following statements would be correct? The U.S. rate of oil consumption per capita was about:

(i) 2 times the world rate.

(ii) 5 times the world rate.

(iii) 10 times the world rate.

(iv) 50 times the world rate.

(c) There are 42 gallons in a barrel of oil. Which of the following statements is true? The average American is responsible for about:

(i) 0.5 gallons of oil use per day.

(ii) 2.5 gallons of oil use per day.

(iii) 5 gallons of oil use per day.

(iv) 50 gallons of oil use per day.

MAKING CONNECTIONS ACROSS THE COURSE

(7) People often confuse the words million, billion, and trillion when speaking. An estimate can help you decide if the speaker uses the correct word. Consider this situation: A speaker says, “The U.S. federal debt is $18 billion dollars. That’s over $56,000 for every person in the country.”

Select the correct statement from the choices below. (Note: When you say the numbers are consistent, you mean that they make sense in relation to each other. Assume there are approximately 321 million people in the U.S.)

(i) The two numbers in the statement are consistent with each other.

(ii) The two numbers in the statement are not consistent. If the debt is $56,000 per capita, the total debt must be $18 million.

(iii) The two numbers in the statement are not consistent. If the debt is $56,000 per capita, the total debt must be $18 trillion.

(8) Terrence is very careful about tracking his gas mileage. Every time he fills his gas tank, he records how much gas he buys and the number of miles he has driven. He puts this information into a spreadsheet so he can easily calculate his gas mileage in miles per gallon.

Screen capture of data in an excel sheet, indicating the following in cells: A1 = Number of Miles B1 = Gallons of Gas A2 = 255 B2 = 13.2 A3 = 136 B3 = 5.9 A4 = 297 B4 = 13.5 A5 = 114 B5 = 5.3

(a) Select the formula that would calculate Terrence’s gas mileage.

(i) = (A2 + A3 + A4 + A5) / (B2 + B3 + B4 + B5)

(ii) = A2 + A3 + A4 + A5 / B2 + B3 + B4 + B5

(iii) = (B2 + B3 + B4 + B5) / (A2 + A3 + A4 + A5)

(iv) = B2 + B3 + B4 + B5 / A2 + A3 + A4 + A5

(b) Terrence is planning a long road trip of about 1,000 miles. The average price of gas is $3.85/gallon. Based on the data in the spreadsheet, calculate how much he should budget for gas. Round to the nearest dollar.

(9) The following table was created to compare two internet service plans, Plan A and Plan B. The monthly bill for each plan was computed based on the expected download speeds. While the actual monthly bills are not given, their differences are given in the last column.

Data (Mb)	Plan A	Plan B	Plan A – Plan B
100	*	*	−7.5
500	*	*	−5
750	*	*	−2.5
1000	*	*	0
2000	*	*	10.5

(a) The first entry in the last column is −7.5. Which of the following statements explains what this tells you about Plan A and Plan B?

(i) Plan A costs $7.50 more than Plan B for someone who has a 100Mb plan.

(ii) Plan B costs $7.50 more than Plan A for someone who has a 100Mb plan.

(iii) The Plan A customer used the internet 7½ fewer Mb than the Plan B customer.

(iv) The Plan B customer used the internet 7½ fewer Mb than the Plan A customer.

(b) Further down the last column is the entry 10.5. What does this tell you about Plan A and Plan B? Write your answer as a complete sentence using the Writing Principle.

________________________________________

⁷ https://www.bp.com/content/dam/bp/business-sites/en/global/corporate/pdfs/energy-economics/statistical-review/bp-stats-review-2022-full-report.pdf

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