Tom owns movies on DVD and Blue-ray in a ratio of 7:2. If he buys 6 more Blue-ray movies, the ratio would change to 11:4. How many Blue ray movies did he have to start with?
Please show steps to answer this problem.
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SFtraveler
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ezhilkumarank
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Initial RatioSFtraveler wrote:Tom owns movies on DVD and Blue-ray in a ratio of 7:2. If he buys 6 more Blue-ray movies, the ratio would change to 11:4. How many Blue ray movies did he have to start with?
Please show steps to answer this problem.
DVD : BR
7x: 2x
Adding 6 more BR movies changes the ratio to 11:4.
Hence setting up the equation - (2x+6)/7x = 4/11
=> 22x + 66 = 28x
=> 6x = 66 => x =11
Hence the original number of BR movies was 22 and the final number is 28.
Moving this post to PS forum.
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please move to PS sub-forum.ezhilkumarank wrote:Initial RatioSFtraveler wrote:Tom owns movies on DVD and Blue-ray in a ratio of 7:2. If he buys 6 more Blue-ray movies, the ratio would change to 11:4. How many Blue ray movies did he have to start with?
Please show steps to answer this problem.
DVD : BR
7x: 2x
Adding 6 more BR movies changes the ratio to 11:4.
Hence setting up the equation - (2x+6)/7x = 4/11
=> 22x + 66 = 28x
=> 6x = 66 => x =11
Hence the original number of BR movies was 22 and the final number is 28.
Moving this post to PS forum.
also to cut on time the same approach with couple of reductions -->
D/B=7/2 AND D/(B+6)=11/4
2D=7B AND 4D=11B+66 --> 2*7B=11B+66 --> B=22
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Sneaky but efficient approach:SFtraveler wrote:Tom owns movies on DVD and Blue-ray in a ratio of 7:2. If he buys 6 more Blue-ray movies, the ratio would change to 11:4. How many Blue ray movies did he have to start with?
Please show steps to answer this problem.
Since the DVDs are represented by a 7 and an 11 in the two ratios, the number of DVDs must be a multiple of both 7 and 11.
Thus, it is likely that DVDs = 7*11 = 77.
Thus, Blu-rays = 2*11 = 22, giving us the required ratio of 77:22 = 7:2.
To confirm that these values are correct, the new number of Blu-rays = 22+6 = 28, and the new ratio = 77:28 = 11:4.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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