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20 Sep 2019, 08:18
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C
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76% (02:02) correct
24%
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wrong
based on 164
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Andy and Bob originally had pens in the ratio 3:7. Bob gave some of his pens to Andy. As a result, the ratio of number of pens of Andy and Bob became 2:3. What fraction of his pens did Bob gave to Andy?
A. 1/5
B. 2/9
C. 1/7
D. 2/7
E. 1/6
A. 1/5
B. 2/9
C. 1/7
D. 2/7
E. 1/6
20 Sep 2019, 08:57
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let Andy has \(3x\) pens, and Bob has \(7x\) pens, and Bob gave \(y\) pens to Andy
\(\frac{3x+y}{7x-y} = \frac{2}{3}\)
so \(y = x\), and fraction of his pens did Bob gave to Andy =\(\frac{y}{7x} = \frac{x}{7x} = \frac{1}{7}\)
\(\frac{3x+y}{7x-y} = \frac{2}{3}\)
so \(y = x\), and fraction of his pens did Bob gave to Andy =\(\frac{y}{7x} = \frac{x}{7x} = \frac{1}{7}\)
05 Nov 2020, 23:59
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Dillesh4096
Andy and Bob originally had pens in the ratio 3:7. Bob gave some of his pens to Andy. As a result, the ratio of number of pens of Andy and Bob became 2:3. What fraction of his pens did Bob gave to Andy?
A. 1/5
B. 2/9
C. 1/7
D. 2/7
E. 1/6
Posted from my mobile device
A. 1/5
B. 2/9
C. 1/7
D. 2/7
E. 1/6
Posted from my mobile device
SUBSTITUTION
Let the number of pens be some multiple of (3+7) or 10, say 100.
so A:B=30:70....
After B gave some pens, it becomes 2:3 or 40:60. Clearly B gave 70-60 or 10.
10 as fraction of 70 =\(\frac{10}{70}=\frac{1}{7}\)
ALGEBRAIC
A:B = 3:7 or 3x:7x
Let B gives y pens, so (3x+y):(7x-y)=2:3..
\(\frac{(3x+3y)}{(7x-y)}=\frac{2}{3}\)..
\(9x+3y=14x-2y\)
\(5x=5y....x=y\)
So y as a fraction of 7x => \(\frac{y}{7x}=\frac{x}{7x}=\frac{1}{7}\)
C
