Final answer:
Chester can separate the quartz chess pieces from the Styrofoam packing peanuts by soaking them in water, allowing the denser quartz to sink and the lighter Styrofoam to float, facilitating an easy separation.
Step-by-step explanation:
The main answer for how Chester can separate dense quartz chess pieces from the light and airy Styrofoam packing peanuts is by soaking the contents in water (option d). This method takes advantage of the difference in density between quartz and Styrofoam. Quartz has a higher density than water and will sink, while Styrofoam is less dense than water and will float. This makes it easy to separate the two materials without the need for shaking, which might not be effective, using a vacuum cleaner, which could cause a mess, or applying a strong magnet, which will not affect quartz or Styrofoam.In conclusion, separating the materials by soaking them in water is the most effective and practical approach. Chester can simply remove the quartz chess pieces from the bottom of the container once the Styrofoam packing peanuts have floated to the top.