Problem:

The directors of a dance show expect many students to participate but don’t yet know how many students will come. The directors need 7 students to work on the technical crew. The rest of the students work on dance routines in groups of 9. For the show to work, they need at least 6 full groups working on dance routines.

1. Write and solve an inequality to represent this situation.

2. Write a sentence to the directors about the number of students they need.

Question

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wagonbelleville wagonbelleville · Answer 1 · 2019-01-16T07:00:40+01:00

Answer:

1. 7 + 9x ≥ 54

2. The minimum number of students required are 5.

Step-by-step explanation:

It is given that 7 students are in the technical crew.

Let, the number of students in a group = x

Also, the rest of the students work in dance routines in groups of 9 i.e. total number of students in dance routines is 9x.

Thus, total number of students = 7 + 9x.

As, at least 6 groups are needed i.e. minimum number of students needed are 6×9 = 54.

This gives us the relation,

7 + 9x ≥ 54

i.e. 9x ≥ 54 - 7

i.e. 9x ≥ 47

i.e. x ≥ 5

Hence, the minimum number of students required are 5.

AFOKE88 AFOKE88 · Answer 2 · 2022-03-25T13:35:09+01:00

1) The inequality that represents the situation of the number of students is; 9x + 7 ≥ 54

We are told that there are 7 students in the technical crew.

We will make the number of students in a group = x

Thus, the rest of the students work in dance routines in groups of 9 which means that total number of students in dance routines is 9x.

Thus,

Total number of students = 9x + 7

They need at least 6 full groups working on dance routines. Thus; minimum number of students required = 9 * 6 = 54

Thus, our inequality will be;

9x + 7 ≥ 54

9x ≥ 54 - 7

9x ≥ 47

x ≥ 47/9

We have to approximate to a whole number and so;

x ≥ 6

Hence, the minimum number of students required 6 students

Read more about Inequalities at; https://brainly.com/question/25275758