Question

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
7​ students to work on the technical crew. The rest of the students work on dance routines in groups of
9
9​. For the show to work, they need at least
6
6​ full groups working on dance routines.

a) Write and solve an inequality to represent this situation, and graph the solution on a number line.

Answer 1

Answer:

Step-by-step explanation: Let x represent the total number of students participating in the show. The technical crew requires 7 students, and the number of students working on the dance routines should be at least 6 full groups, which is equivalent to 6 * 9 = 54 students. Therefore, the inequality representing this situation is:

7 + 9g ≥ 54

9g ≥ 47

g ≥ 47/9

g ≥ 5.22

where g represents the number of groups. Since the number of groups must be a whole number, the minimum number of groups to meet the requirement is 6.

The inequality g ≥ 6 represents the number of groups of students working on dance routines.

Graphically, this would be shown as an open circle at g = 6 on the number line, and the region to the right of it shaded to indicate all values greater than or equal to g = 6.