Question

A daycare owner purchased toy boxes A (132 cm), B (94 cm), and C (108 cm) to sit along a wall totaling 456 cm. Two bookcases, D and E, with equal widths will be added. What is the greatest possible width (w) for bookcases D and E?

a) 112 cm
b) 114 cm
c) 116 cm
d) 118 cm

Answer 1

The greatest possible width for each bookcase D and E is 61 cm. Option (c) with a total width of 116 cm for both bookcases is the largest option that does not exceed the possible width for one bookcase, indicating that each will be 58 cm wide.

Step-by-step explanation:

To find the greatest possible width (w) for bookcases D and E, first add the widths of the toy boxes A, B, and C:
132 cm + 94 cm + 108 cm = 334 cm.
Now subtract this total from the total wall length to find the remaining space for the two bookcases:
456 cm - 334 cm = 122 cm.
Since D and E are of equal width, divide this remaining space by 2 to find the greatest possible width for each bookcase:
122 cm / 2 = 61 cm.

Therefore, the greatest possible width for each bookcase, w, is 61 cm, which is not an option listed in the question. However, you should choose the largest width option that does not exceed 61 cm. That would be option (c) 116 cm in total for both D and E, meaning each bookcase would be 58 cm wide.