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QOTD#20 One cup of nuts that contains exactly half peanuts a
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03 Apr 2017, 03:06
03 Apr 2017, 03:06
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Question Stats:
48% (02:05) correct
51% (02:02) wrong based on 43 sessions
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One cup of nuts that contains exactly half peanuts and half cashews is added to a bowl of nuts that is exactly one third peanuts, one third cashews, and one third almonds. This results in a three-cup mixture of nuts. What fraction of the new nut mixture is peanuts?
Drill 3
Question: 3
Page: 318
Question: 3
Page: 318
Show: :: OA
\(\frac{7}{18}\)
Re: QOTD#20 One cup of nuts that contains exactly half peanuts a
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03 Apr 2017, 05:28
03 Apr 2017, 05:28
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Explanation
The total mixture contains three cups, so the second bowl must contain two cups.
This 2-cup bowl of nuts divided into even thirds consists of \(\frac{2}{3}\)cups peanuts, cups cashews, \(\frac{2}{3}\) and \(\frac{2}{3}\) cups almonds.
Combining this with the 1-cup mixture of \(\frac{1}{2}\) cup peanuts and \(\frac{1}{2}\) cup cashews results in \(\frac{7}{6}\) cups peanuts in a 3-cup mixture.
So, \(\frac{6}{3}=\frac{7}{18}\) of the new nut mixture is peanuts.
Hence \(\frac{7}{18}\) is correct.
The total mixture contains three cups, so the second bowl must contain two cups.
This 2-cup bowl of nuts divided into even thirds consists of \(\frac{2}{3}\)cups peanuts, cups cashews, \(\frac{2}{3}\) and \(\frac{2}{3}\) cups almonds.
Combining this with the 1-cup mixture of \(\frac{1}{2}\) cup peanuts and \(\frac{1}{2}\) cup cashews results in \(\frac{7}{6}\) cups peanuts in a 3-cup mixture.
So, \(\frac{6}{3}=\frac{7}{18}\) of the new nut mixture is peanuts.
Hence \(\frac{7}{18}\) is correct.
Re: QOTD#20 One cup of nuts that contains exactly half peanuts a
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01 Jan 2019, 16:46
01 Jan 2019, 16:46
sandy wrote:
Explanation
Combining this with the 1-cup mixture of \(\frac{1}{2}\) cup peanuts and \(\frac{1}{2}\) cup cashews results in \(\frac{7}{6}\) cups peanuts in a 3-cup mixture.
So, \(\frac{6}{3}=\frac{7}{18}\) of the new nut mixture is peanuts.
Hence \(\frac{7}{18}\) is correct.
Combining this with the 1-cup mixture of \(\frac{1}{2}\) cup peanuts and \(\frac{1}{2}\) cup cashews results in \(\frac{7}{6}\) cups peanuts in a 3-cup mixture.
So, \(\frac{6}{3}=\frac{7}{18}\) of the new nut mixture is peanuts.
Hence \(\frac{7}{18}\) is correct.
Please elaborate.
