Julia is hanging a bookcase on the wall that holds her digital video disc (DVD) collection where each DVD in its case weighs the same. The weight of the bookcase with 10 DVDs is 30.4 pounds, and the weight of the bookcase with
45 DVDs is 38.8 pounds. If the anchors holding the bookcase can support up to 100 pounds, how many DVDs can the bookcase hold? (1 point)
0 416
0 200
© 300-
100
Let's let x be the weight of each DVD in its case.
10x + 30.4 = 38.8
10x = 8.4
x = <<0.84=0.84>>0.84 pounds
So each DVD weighs 0.84 pounds.
We can now find the maximum number of DVDs the bookcase can hold.
100 - 30.4 = 69.6 pounds can be allocated for DVDs.
69.6 / 0.84 = <<69.6/0.84=83.81>>83.81
Therefore, the bookcase can hold a maximum of 83 DVDs. Answer: \boxed{08380}.