Section C Section C Checkpoint

Problem 1

There are 50 states in the U.S.

  1. 46% of all the states have an ocean coastline. How many states is this? Show your reasoning.
  2. There are 7 states with a lake shoreline. What percentage of all the states is this?
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Solution

  1. 23 states. Sample reasoning:

    • The ratio 23 to 50 is equivalent to 46 to 100.
    • number of states percentage
      50 100
      1 2
      23 46
    • 46100⋅50=23\frac{46}{100} \boldcdot 50 =23

  2. 14% of all the states. Sample reasoning:

    • The ratio 7 to 50 is equivalent to 14 to 100.
    • If 50 states is 100% of all the states, then 1 state is 2% of all the states and 7 states is 7⋅27 \boldcdot 2 or 14% of all the states.
Show Sample Response
Sample Response

  1. 23 states. Sample reasoning:

    • The ratio 23 to 50 is equivalent to 46 to 100.
    • number of states percentage
      50 100
      1 2
      23 46
    • 46100⋅50=23\frac{46}{100} \boldcdot 50 =23

  2. 14% of all the states. Sample reasoning:

    • The ratio 7 to 50 is equivalent to 14 to 100.
    • If 50 states is 100% of all the states, then 1 state is 2% of all the states and 7 states is 7⋅27 \boldcdot 2 or 14% of all the states.

Problem 2

Priya has a plant that measures 26 cm tall. This is 130% as tall as its height when Priya bought it. How tall was the plant when it was bought? Show your reasoning.
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Solution

20 cm. Sample reasoning:

  1. Using a double number line diagram:

  2. Using a table:

    height (cm) percentage
    26 130
    2 10
    20 100
Show Sample Response
Sample Response

20 cm. Sample reasoning:

  1. Using a double number line diagram:

  2. Using a table:

    height (cm) percentage
    26 130
    2 10
    20 100