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16 Sep 2014, 00:14
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60 percent of the people surveyed said that they would vote for Stewart. Of those who said they would vote for Stewart, 90 percent actually voted for him, and of those who did not say that they would vote for Stewart, 5 percent actually voted for him. What percent of the group surveyed voted for Stewart?
A. 30%
B. 40%
C. 50%
D. 56%
E. 64%
A. 30%
B. 40%
C. 50%
D. 56%
E. 64%
16 Sep 2014, 00:14
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Official Solution:
60 percent of the people surveyed said that they would vote for Stewart. Of those who said they would vote for Stewart, 90 percent actually voted for him, and of those who did not say that they would vote for Stewart, 5 percent actually voted for him. What percent of the group surveyed voted for Stewart?
A. 30%
B. 40%
C. 50%
D. 56%
E. 64%
Let \(x\) be the total number of people polled.
• \(0.6x\) people say that they will vote for Stewart.
• Of those, \(0.9*0.6x = 0.54x\) actually voted for him.
• \(0.4x\) people say that they will not vote for Stewart.
• Of those, \(0.05*0.4x = 0.02x\) nevertheless voted for him.
So, the total percentage of people who voted for Stewart is \(0.54x + 0.02x = 0.56x\) or 56%.
Answer: D
60 percent of the people surveyed said that they would vote for Stewart. Of those who said they would vote for Stewart, 90 percent actually voted for him, and of those who did not say that they would vote for Stewart, 5 percent actually voted for him. What percent of the group surveyed voted for Stewart?
A. 30%
B. 40%
C. 50%
D. 56%
E. 64%
Let \(x\) be the total number of people polled.
• \(0.6x\) people say that they will vote for Stewart.
• Of those, \(0.9*0.6x = 0.54x\) actually voted for him.
• \(0.4x\) people say that they will not vote for Stewart.
• Of those, \(0.05*0.4x = 0.02x\) nevertheless voted for him.
So, the total percentage of people who voted for Stewart is \(0.54x + 0.02x = 0.56x\) or 56%.
Answer: D
09 Aug 2023, 10:06
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I think this is a high-quality question and I agree with explanation.
