Question

A rectangular piece of tin has an area of 1,012 square inches. A square of 4 inches is cut from each corner, and an open box is made by turning up the ends and sides. If the volume of the box is 2,128 cubic inches, what were the original dimensions of the piece of tin? A. 22 in by 46 in B. 14 in by 34 in C. 18 in by 42 in D. 26 in by 50 in

Answer 1

4(x - 8)(1,012/x - 8) = 2,128

(x - 8)(1,012/x - 8) = 532

1,012 - 8x - 8,096/x + 64 = 532

1076 - 8x - 8,096/x = 532

8x + 8,096/x = 544

8x² - 544x + 8,096 = 0

x² - 68x + 1,012 = 0

(x - 22)(x - 46) = 0

x = 22, 46

The original dimensions of the box were 22 in. by 46 in.

The correct answer is A.