Rational Expressions and Functions

Question

Unit Portfolio
Directions: Complete each of the tasks outlined below.
Task 1
Volume and surface area are often compared by manufacturers in order to
maximize how much of something can go inside of a package (volume) while
keeping how much material is required to create the package (surface area) low.
Pick a product that might be packaged in the shape of a rectangular prism. A
rectangular prism has three dimensions: length, width, and height. The surface
area of a rectangular prism can be found using the formula SA = 2lw + 2wh + 2lh.
The volume of a rectangular prism can be found using the formula V = lwh. Write
an expression for the ratio of surface area to volume for the figure.
Choose an appropriate length, width, and height for your package so that it can fit
the product you are shipping. Using these dimensions, what is the ratio of surface
area to volume?
Task 2
John, Rick, and Molli paint a room together.
a. Pick a reasonable amount of time in which the three friends can paint the
room together. Also pick a reasonable amount of time in which John can
paint the room alone and a reasonable amount of time in which Rick can
paint the room alone.
b. What is the hourly rate for John, Rick, and Molli (when working
together)? Use rooms per hour as the unit for your rates.
c. What is the hourly rate for John? What is the hourly rate for Rick? Refer
to the amount of time you determined in which John and Rick can paint
the room alone. Use rooms per hour as the unit for your rates.
d. Write an equation comparing the group rate to the sum of the individual
rates. How should the group rate and the sum of the individual parts
compare? Use parts (b) and (c) to help you write the equation.
e. What is the least common denominator for the equation you found in part (c)?
f. Solve the equation and determine how long it will take Molli to paint the
room alone.
Task 3
Suppose you are having a birthday party at the local bowling alley. You are trying
to figure out how many people you can afford to invite.
a. The number of guests you can invite to your party varies inversely with the
price per bowler at the alley. Explain what this means.
b. How much money are you willing to spend to host this bowling party?
c. Set up an equation that shows the inverse relationship between the number
of guests at your party and the price per bowler. Your answer to part (b)
should be part of this equation.
d. Research two local bowling alleys. Record the price per bowler at each of
these two alleys.
Calculate how many guests you will be able to invite to your party at each of the
bowling alleys. Which alley would you choose for your party? Why?

Answer 1

Task 1:

Product: A box of cereal

Dimensions: Length = 10 inches, Width = 4 inches, Height = 12 inches

Surface Area: SA = 2lw + 2wh + 2lh = 2(10)(4) + 2(4)(12) + 2(10)(12) = 328 square inches

Volume: V = lwh = (10)(4)(12) = 480 cubic inches

Ratio of Surface Area to Volume: SA/V = 328/480 = 0.6833

Task 2:

a. Reasonable amount of time: 4 hours

John's time alone: 6 hours

Rick's time alone: 8 hours

b. Group rate: 1/4 room per hour

c. John's rate: 1/6 room per hour

Rick's rate: 1/8 room per hour

d. Group rate = John's rate + Rick's rate + Molli's rate

1/4 = 1/6 + 1/8 + Molli's rate

e. Least common denominator: 24

f. Solving the equation:

1/4 - 1/6 - 1/8 = Molli's rate

1/24 = Molli's rate

Molli can paint the room alone in 24 hours.

Task 3:

a. Inverse relationship means that as one variable increases, the other variable decreases. In this case, as the price per bowler at the alley increases, the number of guests that can be invited decreases.

b. $200

c. Let x be the number of guests and y be the price per bowler. Then, we have:

xy = 200

d.

Bowling Alley 1: $5 per bowler

Number of guests: x = 200/5 = 40 guests

Bowling Alley 2: $6 per bowler

Number of guests: x = 200/6 = 33.33 guests (rounded down to 33)

I would choose Bowling Alley 1 because it can accommodate more guests within my budget.

Answer 2

Which of the following describes a claim?(1 point)
Responses

a statement that connects evidence to a reason
a statement that connects evidence to a reason

a statement that presents the speaker’s position or opinion
a statement that presents the speaker’s position or opinion

a statement that will grab the audience's attention
a statement that will grab the audience's attention

a statement that everyone in the audience will agree with

Answer 3

a statement that presents the speaker’s position or opinion