Question

Adam needs both small and large cones to set up for a soccer practice. He knows there are fewer than 30 cones in the storage room. He needs at least a dozen large cones. Let x represent the number of small cones and y represent the number of large cones. Select all inequalities that model this situation.

x>0  
   y≥12
 x+y≤30
  y>12
  x≥0
 x+y<30

Answer 1

x: the number of small cones
y: the number of large cones

a "dozen" means 12.


"Adam needs both small and large cones to set up for a soccer practice" mean that x must not be 0, and y must not be 0.

"there are fewer than 30 cones in the storage room." mean that : x+y<30

"He needs at least a dozen large cones." means that y≥12

so we have:

i) x≠0, y≠0, that is x>0, y>0

ii) x+y<30

iii) y≥12


now let's check all choices we have:

x>0 True by i
y≥12 True by iii
x+y≤30 Not True by ii (x+y is smaller than 30, the sum cannot be 30)
y>12 Not true by iii (y may be = 12)
x≥0 Not true by i, Adam needs small cones to (so we are assuming there are some in the storage room. Though this is open to interpretation)
x+y<30 True