Section C Section C Checkpoint

Problem 1

A painter mixes 3 cups of black paint and 20 cups of white paint to make a batch of gray paint.

  1. Complete the double number line diagram to show the amount of each color needed to make 5 batches of the gray paint.

  2. If the painter has 18 cups of black paint, how many cups of white paint are needed to make the same shade of gray?
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Solution

  1. 15 cups of black paint and 100 cups of white paint for 5 batches

  2. 120 cups of white paint
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Sample Response

  1. 15 cups of black paint and 100 cups of white paint for 5 batches

  2. 120 cups of white paint

Problem 2

At a carnival, it costs $5 for 4 people to play a game. What is the cost per person?

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Solution

Sample responses:

  • It costs $1.25 per person to play a game.
  • The carnival charges $1.25 per person for a game.
Show Sample Response
Sample Response

Sample responses:

  • It costs $1.25 per person to play a game.
  • The carnival charges $1.25 per person for a game.

Problem 3

Diego and Priya each rode their bicycle at a constant speed. Diego traveled 7 kilometers in 60 minutes. Priya traveled 2 kilometers in 15 minutes.

Did they travel at the same rate? Explain your reasoning.

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Solution

No, they did not travel at the same rate. Priya traveled faster. Sample reasoning:

  • There are four 15 minutes in 60 minutes, so Priya would travel 4⋅24 \boldcdot 2, or 8, kilometers in 60 minutes, 1 kilometer more than Diego traveled in that amount of time.

  • Using a double number line, we can see that Priya would ride 8 kilometers in 60 minutes, while Diego rode 7 kilometers in 60 minutes.

  • Diego biked 74\frac{7}{4} or 1.75 kilometers in 15 minutes, which is a shorter distance than Priya traveled in 15 minutes.
Show Sample Response
Sample Response

No, they did not travel at the same rate. Priya traveled faster. Sample reasoning:

  • There are four 15 minutes in 60 minutes, so Priya would travel 4⋅24 \boldcdot 2, or 8, kilometers in 60 minutes, 1 kilometer more than Diego traveled in that amount of time.

  • Using a double number line, we can see that Priya would ride 8 kilometers in 60 minutes, while Diego rode 7 kilometers in 60 minutes.

  • Diego biked 74\frac{7}{4} or 1.75 kilometers in 15 minutes, which is a shorter distance than Priya traveled in 15 minutes.