Ruby, the chief packer at the Booster Button Company, is packing booster buttons for four football teams. She has four different shaped boxes, one for each team's buttons. Each of the four boxes has a volume of 96 cubic inches and dimensions that are whole numbers greater than one. As Ruby packed the buttons, she made the following mental notes:
The Red Raiders' box is 12 inches long and has the greatest surface area.
The box whose top measures 4 inches by 6 inches isn't the Blue Streaks' box.
The Green Wave's box has the smallest surface area.
One face of the Orange Tiger's box has a surface area of 32 square inches.
What are the dimensions of each team's box?
Reference from Greenes, Carol, Linda Schulman, Rika Spungin, Suzanne Chapin, Carol Findell. Mathletics: Gold Metal Problems. Providence RI: Janson Publications Inc., 1990. p. 61.