Lesson 17

Negative Rates

Problem 1

Describe a situation where each of the following quantities might be useful.

  1. -20 gallons per hour
  2. -10 feet per minute
  3. -0.1 kilograms per second

Solution

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Problem 2

A bank charges a service fee of $7.50 per month for a checking account.

A bank account has $85.00. If no money is deposited or withdrawn except the service charge, how many months until the account balance is negative?

Solution

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Problem 3

A submarine is searching for underwater features. It is accompanied by a small aircraft and an underwater robotic vehicle.

At one time the aircraft is 200 m above the surface, the submarine is 55 m below the surface, and the underwater robotic vehicle is 227 m below the surface.

  1. What is the difference in height between the submarine and the aircraft?
  2. What is the distance between the underwater robotic vehicle and the submarine?

Solution

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(From Unit 7, Lesson 10.)

Problem 4

Evaluate each expression. When the answer is not a whole number, write your answer as a fraction.

  1. \(\text-4 \boldcdot \text-6\)
  2. \(\text-24 \boldcdot \frac {\text{-}7}{6}\)
  3. \(4 \div \text-6\)
  4. \(\frac43 \div \text-24\)

Solution

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(From Unit 7, Lesson 16.)

Problem 5

  1. A restaurant bill is $21. You leave a 15% tip. How much do you pay including the tip?
  2. Which of the following represents the amount a customer pays including the tip of 15% if the bill was \(b\) dollars? Select all that apply.

  • \(15b\)
  • \(b+0.15b\)
  • \(1.15b\)
  • \(1.015b\)
  • \(b+\frac{15}{100}b\)
  • \(b+0.15\)
  • \(0.15b\)

Solution

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(From Unit 6, Lesson 7.)

Problem 6

Consider a rectangular prism with length 4 and width and height \(d\).

  1. Find an expression for the volume of the prism in terms of \(d\).
  2. Compute the volume of the prism when \(d=1\), when \(d=2\), and when \(d=\frac12\).

A rectangular prism with a square base. The width of the base is labeled d and the rectangular face has length 4 and height d.

Solution

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(From Unit 4, Lesson 15.)