Lesson 10

Comparing Situations by Examining Ratios

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Problem 1

A slug travels 3 centimeters in 3 seconds. A snail travels 6 centimeters in 6 seconds. Both travel at constant speeds. Mai says, “The snail was traveling faster because it went a greater distance.” Do you agree with Mai? Explain or show your reasoning.

Solution

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Problem 2

If you blend 2 scoops of chocolate ice cream with 1 cup of milk, you get a milkshake with a stronger chocolate flavor than if you blended 3 scoops of chocolate ice cream with 2 cups of milk. Explain or show why.

Solution

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Problem 3

There are 2 mixtures of light purple paint.

  • Mixture A is made with 5 cups of purple paint and 2 cups of white paint.
  • Mixture B is made with 15 cups of purple paint and 8 cups of white paint.

Which mixture is a lighter shade of purple? Explain your reasoning.

Solution

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Problem 4

Tulip bulbs are on sale at store A, at 5 for $11.00, and the regular price at store B is 6 for $13. Is each store pricing tulip bulbs at the same rate? Explain how you know.

Solution

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Problem 5

A plane travels at a constant speed. It takes 6 hours to travel 3,360 miles.

  1. What is the plane’s speed in miles per hour?
  2. At this rate, how many miles can it travel in 10 hours?

Solution

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(From Unit 2, Lesson 9.)

Problem 6

A pound of ground beef costs $5. At this rate, what is the cost of:

  1. 3 pounds?
  2. \(\frac 1 2\) pound?
  3. \(\frac 1 4\) pound?
  4. \(\frac 3 4\) pound?
  5. \(3 \frac 3 4\) pounds?

Solution

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(From Unit 2, Lesson 8.)

Problem 7

In a triple batch of a spice mix, there are 6 teaspoons of garlic powder and 15 teaspoons of salt. Answer the following questions about the mix. If you get stuck, create a double number line.

  1. How much garlic powder is used with 5 teaspoons of salt?
  2. How much salt is used with 8 teaspoons of garlic powder?
  3. If there are 14 teaspoons of spice mix, how much salt is in it?
  4. How much more salt is there than garlic powder if 6 teaspoons of garlic powder are used?

Solution

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(From Unit 2, Lesson 7.)