Sienna has four × as many DVDs as Teri. Robert has half as many DVDs as Teri. If Robert has 32 DVDs, how many DVDs does Sienna have?
Sienna has 256 DVDs.
The problem statement declares that Sienna has four times as many DVDs as Teri. It also states that Robert has half as many DVDs as Teri, and Robert has 32 DVDs. Therefore, Teri has twice as many DVDs as Robert, which is 64 DVDs. As Sienna has four times as many DVDs as Teri, she would have 4 * 64 = 256 DVDs.
This would be the incorrect choice as it does not adhere to the given conditions in the question. Given that Robert has 32 DVDs, Teri, having twice as many DVDs as Robert, would have 64 DVDs. Consequently, Sienna, who has four times as many as Teri, would have more than 4 DVDs.
This option is also incorrect. If Robert has 32 DVDs, this would mean that Teri has 64 DVDs because she has twice as many DVDs as Robert. Therefore, Sienna, who has four times as many DVDs as Teri, would have more than 16 DVDs.
This is the incorrect choice because it is the number of DVDs that Teri has, not Sienna. The problem statement states that Teri has twice as many DVDs as Robert, which means she has 64 DVDs. Sienna, however, has four times as many DVDs as Teri, so she would have more than 64 DVDs.
This is the correct choice. Given that Robert has 32 DVDs and Teri has twice as many DVDs as Robert, Teri would have 64 DVDs. Since Sienna has four times as many DVDs as Teri, she would therefore have 4 * 64 = 256 DVDs.
The question requires understanding of proportional relationships. Given that Robert has 32 DVDs and that Teri has twice as many DVDs as Robert, Teri would therefore have 64 DVDs. And since Sienna has four times as many DVDs as Teri, Sienna would have 256 DVDs. The number of DVDs each person has is determined by these proportional relationships.
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