Perform

Now that you’ve seen the variety of ways in which the SAT can test you on linear inequalities, try the following questions to check your understanding. Give yourself 2 minutes to tackle these two questions.

6. If , then what is one possible value of 12h − 4 ?

   

7. Sarah and Zena are head sales associates at a dance apparel shop. In addition to their annual raises, the two will be eligible for holiday bonuses if their dance tops and pants sales meet the following criteria in December: Between the two of them, the girls must sell an average of at least 75 items each, and their combined generated revenue must be at least $6,000. Each top costs $35, and each pair of pants costs $60. If Sarah sells t_S tops and p_S pairs of pants and Zena sells t_Z tops and p_Z pairs of pants, which of the following systems of inequalities correctly depicts the minimum quantities the two must sell to earn a holiday bonus?

   1. t_S + p_S + t_Z + p_Z ≥ 75 
      35(t_S + t_Z) + 60(p_S + p_Z) ≥ 3,000
   2. t_S + p_S + t_Z + p_Z ≥ 150
      90(t_S + p_S + t_Z + p_Z) ≥ 6,000
   3. t_S + p_S + t_Z + p_Z ≥ 150
      35(t_S + t_Z) + 60(p_S + p_Z) ≥ 6,000
   4. t_S + p_S + t_Z + p_Z ≥ 150
      35(t_S + p_S) + 60(t_Z + p_Z) ≥ 6,000