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20 Jul 2010, 02:27
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How do I write two equations and two unknowns (which includes using a ratio relationship) to answer this. On page 57 (Chapter covering Ratios) of the Manhattan Word Translations book, there is the following question:
"The ratio of men to women in a room is 3:4. If there are 56 people in the room, how many of the people are men?"
Okay, clearly you can just do \(3/7 of 56\) to get the number of men in the room. MGMAT also explains step-by-step how you can you use the 'Unknown Multiplier' approach to find the answer. I am, however, stuck on their suggestion that the question can additionally be solved using a ratio relationship.
They state: \(M (for men)/ W (for women)= 3/4\). Together with \(M + W= Total=56\), you can solve for M (and W, for that matter). The algebra for these "two equations and two unknowns" is not too difficult..." Could some please show how to do this 'two equations and two unknowns' approach.
"The ratio of men to women in a room is 3:4. If there are 56 people in the room, how many of the people are men?"
24 men
Okay, clearly you can just do \(3/7 of 56\) to get the number of men in the room. MGMAT also explains step-by-step how you can you use the 'Unknown Multiplier' approach to find the answer. I am, however, stuck on their suggestion that the question can additionally be solved using a ratio relationship.
They state: \(M (for men)/ W (for women)= 3/4\). Together with \(M + W= Total=56\), you can solve for M (and W, for that matter). The algebra for these "two equations and two unknowns" is not too difficult..." Could some please show how to do this 'two equations and two unknowns' approach.
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Hi there,
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20 Jul 2010, 03:31
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M (for Men)/ W (for women) = 3/4 --- (a)
Now as per question total number of people = 56
i.e. M + W = 56 --- (b)
Using equation (a)
4M = 3W
=> 4/3(M) = W
Using value of W in equation in (b)
M + 4/3(M) = 56
7/3(M) = 56
M = 56 * 3 /7 = 24
Hope this helps!!
Now as per question total number of people = 56
i.e. M + W = 56 --- (b)
Using equation (a)
4M = 3W
=> 4/3(M) = W
Using value of W in equation in (b)
M + 4/3(M) = 56
7/3(M) = 56
M = 56 * 3 /7 = 24
Hope this helps!!
20 Jul 2010, 05:00
Kudos
Bookmarks
Perfection! Thanks a lot Varun for the solid explanation, just what I was after, kudos 
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
