Which situations could represent the inequality

x−4<20, where x is a positive integer? Select all that apply. 7.PAFR.2.1

Leighton has 20 pieces of candy in her pocket, 4 of which were given to her by Alan.

AJ has fewer than 20 trading cards in his collection after giving 4 of them to his friend Jaden.

Candace has less than 20 dollars in her wallet after she spent $4 on a bag of chips and a soda.

Sarah must make at least 20 cupcakes for her school bake sale, but she dropped 4 of them on the floor.

1 answer

To analyze which situations represent the inequality \( x - 4 < 20 \), we first simplify the inequality:

\[ x - 4 < 20 \implies x < 24 \]

Thus, \( x \) must be a positive integer less than 24.

Now, let's evaluate each situation provided:

  1. Leighton has 20 pieces of candy in her pocket, 4 of which were given to her by Alan.

    • This means she has \( 20 - 4 = 16 \) pieces of candy remaining.
    • Here, \( x = 16 \), which satisfies \( x < 24 \).
    • This situation represents the inequality.
  2. AJ has fewer than 20 trading cards in his collection after giving 4 of them to his friend Jaden.

    • Let's say AJ originally had \( x \) cards. After giving away 4, he has \( x - 4 < 20 \).
    • However, this can be rearranged to \( x < 24 \), which satisfies the condition.
    • Therefore, this situation represents the inequality.
  3. Candace has less than 20 dollars in her wallet after she spent $4 on a bag of chips and a soda.

    • If we let \( x \) represent the amount of money Candace originally had, then after spending $4, she has \( x - 4 < 20 \).
    • Rearranging gives \( x < 24 \), which indicates that this situation also represents the inequality.
  4. Sarah must make at least 20 cupcakes for her school bake sale, but she dropped 4 of them on the floor.

    • If we let \( x \) represent the number of cupcakes she made, she had \( x - 4 \) left after dropping them.
    • The statement suggests she still needs to have \( x - 4 \geq 16 \); however, it gives no information that directly corresponds with \( x < 24\).
    • Rather, it states she needs to make at least 20 cupcakes initially, implying \( x \geq 20 \).
    • Therefore, this situation does not represent the inequality.

Final Selections:

  • Situations 1, 2, and 3 represent the inequality \( x - 4 < 20 \).