Answer: He can buy 8 DVD's.
Step-by-step explanation:
Since, The number N of DVDs Phil can buy is inversely proportional to the cost C of a DVD.
Thus, [tex]N \propto \frac{1}{C}[/tex]
⇒ [tex]N = \frac{k}{C}[/tex] ------- (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),
[tex]10 = \frac{k}{16}[/tex]
⇒ 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) )
[tex]N = \frac{160}{C}[/tex]
If C = $20,
⇒ [tex]N = \frac{160}{20}[/tex] = 8
Therefore, If the cost of one DVD is $20, he can buy 8 DVD's.
