A distributor ships DVDs to several stores. The shipping boxes contain several DVDs (in their cases) plus a layer of padding at each end of the box. The DVD cases and layers of padding can be arranged neatly inside each box. Each DVD case is 14mm (millimeters) thick, each layer of padding is 10mm, space, m, m thick, and the length of the interior of the box is 132mm, space, m, m. If d represents the number of DVDs that the distributor can fit into one box with two layers of padding, which of the following inequalities best models the situation?

A. 10d+14 ≤ 132
B. 14d+20 ≤ 132
C. 20d+14 ≤ 132
D. 14d+10 ≤ 132

Option B.

Step-by-step explanation:

It is given that,

Thickness of Each DVD case = 14 mm

Thickness of each layer of padding = 10 mm

Length of the interior of the box = 132 mm

Let d represents the number of DVDs that the distributor can fit into one box with two layers of padding.

Thickness of d DVD cases = 14d mm

Thickness of two layers of padding = 10×2=20 mm

Total thickness of d DVD cases and 2 layers of padding = 14d+20

Total thickness must be less than or equal to 132.

Therefore, the correct option is B.

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