Lesson 10

Comparing Situations by Examining Ratios

Let’s use ratios to compare situations.

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.

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.

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.

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.

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?
(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?
(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?
(From Unit 2, Lesson 7.)