Question

A student is hanging a bookcase on the wall that holds their 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?


This is from the Writing Linear Functions Unit Test from Connections Academy 8th grade question 11
PLZ HELP MEEE

Answer 1

The given values indicate that the relationship between the number of

DVDs and the weight of the bookcase is not proportional but linear.

The number of DVDs the bookcase can hold is 300 DVDs.

Reason:

Weight of bookcase with 10 DVDs = 30.4 pounds

Weight of the bookcase with 45 DVDs = 38.8 pounds

Let C represent the weight of the bookcase with no DVDs on it, and let x

represent the weight of one DVD, we have;

30.4 = 10·x + C...(1)

38.8 = 45·x + C...(2)

Subtracting equation (1) from (2) gives;

45·x - 10·x = 38.8 - 30.4

35·x = 8.4

$x = \dfrac{8.4}{35} =0.24$

The weight of each DVD, x = 0.24 pounds

From equation (1), we get;

30.4 = 10·x + C

C = 30.4 - 10·x

C = 30.4 - 10× 2.4 = 28

The weight of the bookcase, C = 28

Let n represent the maximum number of DVDs the bookcase can hold,

which together with the bookcase weigh 100 pounds, we have;

100 = 0.24·n + 28

0.24·n = 100 - 28 = 72

$n = \dfrac{72}{0.24} = 300$

The number of DVDs the bookcase can hold, n = 300 DVDs

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