Hello everyone,
I was reviewing some quant/math basics on the MGRE and I had an issue understanding a quick ratio example where the number of men to women was represented as 3m = 2w. The question was asked, "What is the ration of men to women?" The answer was stated as m/w = 2/3. I'm having trouble because I thought the ratio would be m/w = 3/2. Not sure why this is puzzling me because I had no problem understanding the next ratio example with students/teachers, but I wanted to make sure I understand the foundations correctly.
The ratio in question occurs at the 01;27;29 time on the video.
Thanks for all your help and advise in advance.
Ryan
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- ryandonahue
- Course Students
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- Joined: Tue May 08, 2012 7:00 am
- glenda.lezeau
- Prospective Students
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- Joined: Mon May 07, 2012 6:34 pm
Re: General Ratio question from Foundations of Math Video
Hi Ryan,
I just found the ratio and got 2/3. Double check that your math is correct. What I did was set 3m=2w and then divide w on both sides to get m over w. You will get 3m/w=2. To get the 3 out of the way, multiply its reciprocal to both sides of the equation. So you will multiply 1/3 to both sides and cancel out the 3 on the left. On the right you are multiplying 2 * 1/3 to get 2/3. This part will leave you with m/w=2/3. I hope this helps and clears your confusion. Feel free to ask me any further questions about the steps I took. Good luck!
Glenda
I just found the ratio and got 2/3. Double check that your math is correct. What I did was set 3m=2w and then divide w on both sides to get m over w. You will get 3m/w=2. To get the 3 out of the way, multiply its reciprocal to both sides of the equation. So you will multiply 1/3 to both sides and cancel out the 3 on the left. On the right you are multiplying 2 * 1/3 to get 2/3. This part will leave you with m/w=2/3. I hope this helps and clears your confusion. Feel free to ask me any further questions about the steps I took. Good luck!
Glenda
- ryandonahue
- Course Students
- Posts: 4
- Joined: Tue May 08, 2012 7:00 am
Re: General Ratio question from Foundations of Math Video
Thanks Glenda.
After I read your reply and reviewed my notes I realized my issue was in the initial set up of the problem. I was not comprehending the "=" sign in the equation. I then watched the video and listened to Jen's explanation carefully, especially pertaining to what the men or m need to be equal in quantity to the women w. After that the set up is basic algebra with regards to the fraction m/w. The second example with students to teachers, the dialog already states the ratio for you at 30 to 1 30/1 and that is not the case in Jen's fast example where she states 3m = 2w what is the ratio? of Men to women m/w.
Again thanks for your reply and time.
-Ryan
After I read your reply and reviewed my notes I realized my issue was in the initial set up of the problem. I was not comprehending the "=" sign in the equation. I then watched the video and listened to Jen's explanation carefully, especially pertaining to what the men or m need to be equal in quantity to the women w. After that the set up is basic algebra with regards to the fraction m/w. The second example with students to teachers, the dialog already states the ratio for you at 30 to 1 30/1 and that is not the case in Jen's fast example where she states 3m = 2w what is the ratio? of Men to women m/w.
Again thanks for your reply and time.
-Ryan
- jen
- Manhattan Prep Staff
- Posts: 51
- Joined: Mon Mar 28, 2011 9:50 am
Re: General Ratio question from Foundations of Math Video
Hi, this is Jen! It looks like you guys are on top of this issue. In sum:
If the problem says, "The ratio of cats to dogs is 4 to 5," then cool, that's the ratio, and therefore c/d = 4/5
But if the problem says 6m = 7w, that is an EQUATION, not a ratio. (A ratio of two quantities is also an equation, but one wherein the two variables are presented as a fraction.) You must do simple algebra to get m/w. When you do this, you see that m/w = 7/6, and thus the ratio of men to women is 7 to 6.
Also, importantly, if the ratio of cats to dogs is 4 to 5, the total number of cats and dogs must be a multiple of 9. If the ratio of men to women is 7 to 6, the total number of people must be a multiple of 13. (Add the two ratio parts -- the animals come in "sets" of 4 cats to 5 dogs, and the people come in "sets" of 7 men to 6 women.) Note that this is only true for stuff (people, animals, cars) that must be integers, and not for stuff like liquids, gravel, etc.
Sincerely,
Jen
If the problem says, "The ratio of cats to dogs is 4 to 5," then cool, that's the ratio, and therefore c/d = 4/5
But if the problem says 6m = 7w, that is an EQUATION, not a ratio. (A ratio of two quantities is also an equation, but one wherein the two variables are presented as a fraction.) You must do simple algebra to get m/w. When you do this, you see that m/w = 7/6, and thus the ratio of men to women is 7 to 6.
Also, importantly, if the ratio of cats to dogs is 4 to 5, the total number of cats and dogs must be a multiple of 9. If the ratio of men to women is 7 to 6, the total number of people must be a multiple of 13. (Add the two ratio parts -- the animals come in "sets" of 4 cats to 5 dogs, and the people come in "sets" of 7 men to 6 women.) Note that this is only true for stuff (people, animals, cars) that must be integers, and not for stuff like liquids, gravel, etc.
Sincerely,
Jen
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