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My father asked me this question yesterday, and as a math major I was a little embarrassed that I was not immediately sure that the answer I obtained was correct.

He asked:

If President Trump's overall approval rating is 38% among 125 million total voters, and the approval rating among the 56 million republican voters is 80%, then what is the approval rating of the other 69 million non-republican voters?

Is this a weighted averages sort of problem?

I set up my equation as:

$$0.448\times 0.8 + 0.552 \times x = 0.38$$

Thus $$x= 0.039$$

giving an approval rating of 3.9%.

Is this correct?

FofX
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    Unless I'm missing something, I'd say that this is correct. But..., I'd have also changed names and circumstances to avoid politics in a math web. I'm only telling. – ajotatxe Jul 26 '17 at 01:34
  • you might be able to use https://www.youtube.com/watch?v=_JgfBfHDiNg but I think you may be correct. –  Jul 26 '17 at 01:36
  • Ok thanks, I just literally have not had to answer a question like that in years, wasn't sure if I was going about it incorrectly. @ajotatxe Yea I thought about that, but I just hoped everyone could just focus on the math as it was a legitimate question. I understand where you're coming from though. – FofX Jul 26 '17 at 01:36
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    @ajotatxe: If one presheaf has 80% approval and its colimit ....? – gary Jul 26 '17 at 01:38

1 Answers1

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Yes, this is correct. Maybe this will be more clear:

Total number of approvals: $0.38 \times 125 = 47.5$

Number of approvals among republicans: $0.8 \times 56 = 44.8$

Number of approvals among non-republicans: $x \times 69$

$47.5 = 44.8 + x \times 69$

$x = 0.039$