Question

each equation below is followed by several stories.
select all of the stories that can be represented by the equation.
if none of the stories can be represented, select
one of the above\.
(a) $3x = 12$

• mai had $x$ cards. then her friend gave her 3 cards. mai now has 12 cards.
• mai has 3 friends. each friend gave her $x$ cards. this gave mai 12 cards.
• mai has 3 packs of cards. each pack has $x$ cards. mai has 12 cards.
• mai had $x$ cards. then she gave her friend 3 cards. mai now has 12 cards.
• none of the above

(b) $x - 4 = 16$

• a dog park has 4 sections. each section has $x$ dogs. the park has a total of 16 dogs.
• there were $x$ dogs at a park. then 4 dogs were taken away. there are now 16 dogs in the park.
• there were $x$ dogs at a park. then 4 of the dogs ran outside of the park. there are now 16 dogs left in the park.
• there were $x$ dogs at a park. then 4 other dogs were brought in. there are now 16 dogs at the park.
• none of the above

Explanation:

Part (a)

Step 1: Analyze each story for \( 3x = 12 \)

• Story 1: "Mai had \( x \) cards. Then her friend gave her 3 cards. Mai now has 12 cards."

The equation here would be \( x + 3 = 12 \), not \( 3x = 12 \). So this does not match.

• Story 2: "Mai has 3 friends. Each friend gave her \( x \) cards. This gave Mai 12 cards."

Total cards = \( 3 \times x = 3x \), and total is 12. So \( 3x = 12 \). This matches.

• Story 3: "Mai has 3 packs of cards. Each pack has \( x \) cards. Mai has 12 cards."

Total cards = \( 3 \times x = 3x \), and total is 12. So \( 3x = 12 \). This matches.

• Story 4: "Mai had \( x \) cards. Then she gave her friend 3 cards. Mai now has 12 cards."

The equation here would be \( x - 3 = 12 \), not \( 3x = 12 \). So this does not match.

Part (b)

Step 1: Analyze each story for \( x - 4 = 16 \)

• Story 1: "A dog park has 4 sections. Each section has \( x \) dogs. The park has a total of 16 dogs."

The equation here would be \( 4x = 16 \), not \( x - 4 = 16 \). So this does not match.

• Story 2: "There were \( x \) dogs at a park. Then 4 dogs were taken away. There are now 16 dogs in the park."

After taking away 4, remaining is \( x - 4 \), and this equals 16. So \( x - 4 = 16 \). This matches.

• Story 3: "There were \( x \) dogs at a park. Then 4 of the dogs ran outside of the park. There are now 16 dogs left in the park."

After 4 ran out, remaining is \( x - 4 \), and this equals 16. So \( x - 4 = 16 \). This matches.

• Story 4: "There were \( x \) dogs at a park. Then 4 other dogs were brought in. There are now 16 dogs at the park."

The equation here would be \( x + 4 = 16 \), not \( x - 4 = 16 \). So this does not match.

Answer:

(a):

• Mai has 3 friends. Each friend gave her \( x \) cards. This gave Mai 12 cards.
• Mai has 3 packs of cards. Each pack has \( x \) cards. Mai has 12 cards.