abansal1805 wrote:
A certain cooking oil is composed of olive, canola and grapeseed oils in a ratio of 1:11:22 by weight. If the ratio of olive oil to canola oil is tripled while the ratio of olive oil to grapeseed oil stays the same, what fraction of the new oil will be canola oil?
A. \(\frac{9}{80}\)
B. \(\frac{9}{69}\)
C. \(\frac{11}{80}\)
D. \(\frac{11}{69}\)
E. \(\frac{11}{25}\)
This question requires careful reading.
Original ratio is
O : C : G
1 : 11: 22
The ratio of Olive : Canola is tripled.
\((\frac{Olive}{Canola} = \frac{1}{11} * 3) = (\frac{3olive}{11canola})=\frac{3}{11}\)
Ratio of Grapeseed : Olive stays the same. The ratio is \(\frac{G}{O} = \frac{22}{1}\)
But now there are 3 parts olive oil. We need more grapeseed oil to maintain the ratio:
\(\frac{22G}{(1)O}=\frac{(x)G}{(3)O}=\frac{66G}{(3)O}=\frac{66}{3}\)
Either: Olive, denominator, was multiplied by 3 (1*3--> 3), so do the same to numerator with grapeseed (22*3--> 66), OR
\(\frac{22G}{(1)O}=\frac{x}{3}\)
\(x = (22*3) = 66\)
New ratio among parts
O : C : G
3 : 11: 66
What fraction of the new oil will be canola oil?
\(\frac{C}{(O+C+G)}\)
Total parts: (O + C + G) = 80
Canola = 11
\(\frac{11}{80}\)
Answer C
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