3.6.2: Exercise 3.6

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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) Blood Alcohol Content (BAC) is affected by many different variables.

(ii) Multiplication undoes division.

(iii) The way you solve an equation that contains addition has nothing to do with the way to solve a different equation that contains subtraction.

(iv) An equation is a statement saying that two expressions are equal, so an operation that changes the value of one side must also be done to the other side of the equation.

DEVELOPING SKILLS AND UNDERSTANDING

(2) Find the solution to each of the following:

(a) 3x + 5 = 14

(b) 6x – 5 = 10

(d) $\dfrac{x}{4}$ + 3 = 8

(3) Recall that Blood Alcohol Content (BAC) is a measurement of how much alcohol is in someone’s blood as a percentage. However, police and the public typically omit the language for percent (%) when quoting the BAC and simply say, “BAC is 0.04.”

Write an interpretation of what each of the following BAC values means in terms of the amount of alcohol per 1,000 grams of blood. You may want to refer back to the example in the collaboration.

(a) BAC = 0.1

(b) BAC = 0.02

(4) Use information from the Wikipedia article “Short-term effects of alcohol consumption” (https://en.Wikipedia.org/wiki/Short-term_effects_of_alcohol_consumption) to list effects on an individual having the following BAC. Give at least three effects for each.

(a) BAC = 0.05

(b) BAC = 0.1

(5) Use the Widmark Equation, $B = -0.015t + \left( \dfrac{2.84\cdot N}{W\cdot r}\right)$, to solve this question. Recall that r = 0.68 for men and r = 0.55 for women.

A male student had five glasses of wine at a party. He weighs 160 pounds. How long will it take before his BAC is 0.08?

(i) 1.31 hours

(ii) 2.00 hours

(iii) 2.84 hours

(iv) 3.37 hours

(6) The percentage of Americans who are retired has been increasing over the last several decades. This is causing some concern because health care, Social Security, and other costs will be the responsibility of a smaller group of people. That is, as the percentage of retired people increases, the percentage of working-age people decreases. The following model predicts the percentage of retired people based on demographic data:²³

\[R = \dfrac{t}{588.24} - 3.24\nonumber \]

where R is the percentage (as a decimal) of Americans who are retired in the year t (for example, in 2016, t = 2016). Use this model to complete the table below.

Year	% of Americans who are Retired
(i)	18%
(ii)	21%
(iii)	24%

MAKING CONNECTIONS ACROSS THE COURSE

(7) Crown molding is a decorative trim installed over the joint between the walls of a room and the ceiling. (If you are not sure that you understand the idea, do an Internet search to find an example picture of crown molding). Andy intends to install crown molding around the four sides of the dining room. There will be no gaps. The dining room ceiling is a rectangle with dimensions 14 feet 9 inches by 13 feet. The crown molding is sold in 8-foot lengths that cost $24 each. He decides to purchase enough pieces to allow for 10% waste due to possible mistakes.

(a) What is the perimeter of the dining room? Perimeter is the distance around the room.

(b) How many 8-foot boards are needed?

(8) To answer the following question, use the formula for the perimeter of a rectangle:

P = 2L + 2W

where P = perimeter;

L = Length; and

W = Width

Andy’s house is on a large lot. He bought 100 yards of chain-link fence on sale. He wants to use all of the material to fence in an area in his backyard. He can only make the fenced area 60 feet wide and he wants it to be as long as possible. What is the longest length possible for the sides?

(9) Now, you will return to graphing on a coordinate plane in preparation for Module 4. Label the following items on the coordinate plane given below. For the points, place a dot at the location of the point and label it with the ordered pair.

(a) (–2, 3)

(b) (2, –4)

(d) (0, 2)

(e) (3, 0)

Blank coordinate plane graph with x-axis from -4 to 4 and y-axis from 4 to -4.

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²³ https://www.census.gov/content/dam/Census/library/publications/2020/demo/p25-1144.pdf

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