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.

step-by-step explanation:

you divide the denominator by the numerator on both sides and if the quotients are equal then the fractions are equivalent

45

step-by-step explanation: