Question

An illusionist needs up to 10 volunteers for a show. She needs no fewer than 4 female volunteers. Let x represent the number of female volunteers and y represent the number of male volunteers.
Which inequalities model the situation?
Select all inequalities that model this situation.

A- x + y < 10
B- x + y ≤ 10
C- x > 4
D- x ≥ 4
E- y > 0
G- y ≥ 0

Answer 1

The correct answers are:

B- x + y ≤ 10 ; and D- x ≥ 4

Explanation:

The illusionist needs at least 4 female volunteers.  This means he could use 4 or more; this means x, the number of female volunteers, is greater than or equal to 4:

x ≥ 4

The total of number of volunteers needed is up to 10.  This means the illusionist can use 10 or fewer people; this means the total is less than or equal to 10.

The number of female volunteers is x and the number of male volunteers is y; together they create the expression x+y.  This gives us

x+y ≤ 10

Answer 2

B, D, and E are all inequalities that model the situation