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.

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.