Question

phil has saved some money and is going to buy some DVDs. The number N of DVDs Phil can buy is inversely proportional to the cost C of a DVD. If the cost of one DVD is $16, then he can buy 10. If the cost of one DVD is $20, then how many DVDs can he buy?

Answer 1

Answer: He can buy 8 DVD's.

Explanation:

Since, The number N of DVDs Phil can buy is inversely proportional to the cost C of a DVD.

Thus,
`N \propto (1)/(C)`

⇒
`N = (k)/(C)` ------- (1)

Where k is the proportional constant.

And, According to the question,

If the cost of one DVD is $16, then he can buy 10 DVD,

That is, If C = $16 then N = 10

Put these value in equation (1),

`10 = (k)/(16)`

⇒ k = 160

Thus, the relation between N( number of DVD's ) and C( Cost of DVD's ) is, ( By putting the value of k in equation (1) )

`N = (160)/(C)`

If C = $20,

⇒
`N = (160)/(20)` = 8

Therefore, If the cost of one DVD is $20, he can buy 8 DVD's.