3.2.2: Exercise 3.2

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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) Renting a car is more expensive than driving your own car.

(ii) A small difference in rounding does not make much difference in results.

(iii) A small difference in rounding can significantly change results when working with large numbers.

(iv) You can calculate the cost of gas per mile by dividing the price of gas by the gas mileage of
the car.

DEVELOPING SKILLS AND UNDERSTANDING

(2) In planning a Thanksgiving vacation, you want to rent a car for a week and travel the Pacific Highway from San Francisco to San Diego. You want to return to San Francisco via Las Vegas, Death Valley, and Yosemite National Park. This trip covers approximately 1,500 miles. You plan to return the car with a full tank of gasoline. You are considering two options advertised by Hertz:

Toyota Camry, 39 mpg highway, costs $505.59 plus taxes and fees, totaling $593.28.
Toyota Prius Hybrid, 53 mpg highway, costs $679.49 plus taxes and fees, totaling $849.61.

In both cases, you must purchase gasoline, which costs $4.70 per gallon in California.

(a) Find the total cost of renting and driving the Camry for the trip:

(i) Total gasoline cost is $_________

(ii) Total cost is $_________

(b) Find the total cost of renting and driving the Prius for the trip.

(i) Total gasoline cost is $_________

(ii) Total cost is $_________

(3) The advertised mpg for new cars is based on a speed of 55 mph. As speed increases above 55 mph, the efficiency reduces dramatically.¹²

3% less efficient at 60 mph
17% less efficient at 70 mph

(a) Compare the efficiency of a Toyota Camry (39 mpg highway) versus a Toyota Prius (53 mpg highway) at speeds of 55 mph, 60 mph, and 70 mph. Round to the nearest tenth.

	55 mph	60 mph	70 mph
Camry	39 mpg
Prius	53 mpg

(b) If gasoline costs $4.70 per gallon, how much money would you save by going 60 mph versus 70 mph on the trip of 1,500 miles in the

(i) Camry? $_________

(ii) Prius? $_________

MAKING CONNECTIONS ACROSS THE COURSE

(4) The U.S. Census Bureau posted the following information in 2020:

Nearly 11.6 million children in the United States—16% of all children—live in families with incomes below the federal poverty level ($26,200 a year for a family of four).¹³

(a) The following graph can be used to illustrate the statement from the U.S. Census Bureau. Identify what each section and the full circle represent in terms of the context and the percentage. Section 1 is the darker section.

Circle graph showing two sections. Section 1 = 21% Section 2 = 79%

The full circle represents _____________________________________ and is _______%.

Section 1 represents ________________________________________ and is _______%.

Section 2 represents ________________________________________ and is _______%.

(b) Can the statement from the US Census Bureau be restated to say that 16% of people below the federal poverty level in the United States are children? Select the best answer.

(i) Yes, because the reference value in both statements is the children in the United States.

(ii) Yes, because both statements are about children living in poverty so the percentages are the same. The reference values do not matter.

(iii) No, because the percentage of children is really much higher because families really need much more money than the federal poverty level.

(iv) No, because the reference value in the first statement is the total number of children. The reference value in the second statement is the total number of people below the poverty level.

(c) Based on the information in the paragraph, which of the following is the best estimate for the number of children in the United States in 2020?

(i) 30 million

(ii) 75 million

(iii) 100 million

(iv) There is not enough information to make an estimate.

______________________________________

¹² www.mpgforspeed.com

¹³ https://www.census.gov/library/publications/2021/demo/p60-273.html

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