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)
Responses
100
100
300
300
416
416
200
Using proportional reasoning, we can set up a proportion to solve for the number of DVDs the bookcase can hold.
Let x be the number of DVDs the bookcase can hold.
We can set up the following proportion:
10 DVDs / 30.4 pounds = x DVDs / 38.8 pounds
Simplifying the proportion, we have:
10/30.4 = x/38.8
Cross-multiplying, we have:
30.4x = 10 * 38.8
30.4x = 388
Dividing both sides by 30.4, we get:
x = 388/30.4
x ≈ 12.76
Therefore, the bookcase can hold approximately 12 DVDs.