High School Pre-Cal

Question

A rectangular piece of cardboard is 10 inches longer than it is wide. A
10-inch square is cut from each corner, and the remaining piece is folded to form a box. The volume of the box is 8,750 cubic inches. What was the width of the original piece of cardboard?

A.25 inches

B.35 inchesC.45 inchesD.55 inches

Answer 1

 

 Length L = w+10 for width w.

 

 Post fabrication, the box has length L-20 = w+10-20 = w-10 and width w-20

 

 The volume is 10(w-10)(w-20) = 8750

                            (w-10)(w-20) = 875

                               w^2 - 30w + 200 = 875

                                  w^2 - 30w - 675 = 0

                                 (w+15)(w-45) = 0

                      w+15=0 results in negative measures

                   

w-45 = 0 ----> width w=45

 

  width is 45

  length is 55