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