Question

select all stories that the tape diagram can represent.

a) diego’s family spends $87 on 4 tickets to the fair and a $39 dinner.

b) there are 87 children and 39 adults at a show. the seating in the theater is split into 4 equal sections.

c) andre buys 4 packs of paper clips with 39 paper clips in each. then he gives 87 paper clips to his teacher.

d) lin buys a pack of 87 pencils. she gives 39 to her teacher and shares the remaining pencils between herself and 3 friends.

e) there are 87 first graders in after - care. after 39 students are picked up, the teacher puts the remaining students into 4 groups for an activity.

Explanation:

Step1: Analyze the tape diagram

The tape diagram shows a total of 87, with 4 equal parts (each labeled \( x \)) and a part labeled 39. So the equation represented is \( 4x + 39 = 87 \) (or equivalently, \( 87 - 39 = 4x \)).

Step2: Analyze Option A

Diego's family spends $87 on 4 tickets (each costing LXI0) and a $39 dinner. So total cost: \( 4x + 39 = 87 \). This matches the tape diagram.

Step3: Analyze Option B

There are 87 children and 39 adults. The seating is split into 4 equal sections. The situation here would involve total people (87 + 39) divided into 4 sections, which is a different equation (\( \frac{87 + 39}{4} \)), not matching the tape diagram.

Step4: Analyze Option C

Andre buys 4 packs with 39 in each (total \( 4 \times 39 \)) and gives 87 to his teacher. The equation here would be \( 4 \times 39 - 87 \), which is different from the tape diagram's equation.

Step5: Analyze Option D

Lin buys 87 pencils, gives 39 to her teacher, and shares the remaining (\( 87 - 39 \)) between herself and 3 friends (total 4 people). So the remaining pencils are \( 87 - 39 \), and each person gets \( x \), so \( 4x = 87 - 39 \), which is equivalent to \( 4x + 39 = 87 \). This matches the tape diagram.

Step6: Analyze Option E

There are 87 first graders, 39 are picked up, remaining (\( 87 - 39 \)) are put into 4 groups. So each group has \( x \), so \( 4x = 87 - 39 \), equivalent to \( 4x + 39 = 87 \). This matches the tape diagram.

Answer:

A. Diego’s family spends $87 on 4 tickets to the fair and a $39 dinner.
D. Lin buys a pack of 87 pencils. She gives 39 to her teacher and shares the remaining pencils between herself and 3 friends.
E. There are 87 first graders in after - care. After 39 students are picked up, the teacher puts the remaining students into 4 groups for an activity.