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Arabica coffee costs $0.40 per ounce, while Robusta coffee costs $0.30 per ounce. If a blend of Arabica and Robusta costs $0.33 per ounce, what percentage of the blend is Arabica?
A. 20%
B. 24%
C. 30%
D. 33%
E. 40%
A. 20%
B. 24%
C. 30%
D. 33%
E. 40%
16 Sep 2014, 01:15
Kudos
Bookmarks
Official Solution:
Arabica coffee costs $0.40 per ounce, while Robusta coffee costs $0.30 per ounce. If a blend of Arabica and Robusta costs $0.33 per ounce, what percentage of the blend is Arabica?
A. 20%
B. 24%
C. 30%
D. 33%
E. 40%
Let the blend consist of \(a\) ounces of Arabica and \(r\) ounces of Robusta.
Then the cost per ounce of the blend with \(a\) ounces of Arabica and \(r\) ounces of Robusta would be \(\frac{total \ cost}{weight} = \frac{0.4a + 0.3r}{a + r}\). Since we know that the blend costs $0.33 per ounce, we'd have \(\frac{0.4a + 0.3r}{a + r} = 0.33\), which simplifies to \(0.07a = 0.03r\), leading to \(\frac{a}{r} = \frac{3}{7}\). Consequently, \(\frac{a}{a+r} = \frac{3}{10}\), which means that Arabica constitutes 30% of the blend.
Answer: C
Arabica coffee costs $0.40 per ounce, while Robusta coffee costs $0.30 per ounce. If a blend of Arabica and Robusta costs $0.33 per ounce, what percentage of the blend is Arabica?
A. 20%
B. 24%
C. 30%
D. 33%
E. 40%
Let the blend consist of \(a\) ounces of Arabica and \(r\) ounces of Robusta.
Then the cost per ounce of the blend with \(a\) ounces of Arabica and \(r\) ounces of Robusta would be \(\frac{total \ cost}{weight} = \frac{0.4a + 0.3r}{a + r}\). Since we know that the blend costs $0.33 per ounce, we'd have \(\frac{0.4a + 0.3r}{a + r} = 0.33\), which simplifies to \(0.07a = 0.03r\), leading to \(\frac{a}{r} = \frac{3}{7}\). Consequently, \(\frac{a}{a+r} = \frac{3}{10}\), which means that Arabica constitutes 30% of the blend.
Answer: C
