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Finesse4eva
Junior Member

USA
6 Posts

 Posted - 05/03/2008 :  17:43:12 i recently ran into a problem that made me question whether i understand ratios as well as i think i do ... The question states If a = 2b, 1/2b=c, and 4c = 3d then what is the ratio of d to a? a) 1/3b) 3/4c) 1d) 4/3e) 3 i set up the following ration of a = 2b = 4c = 3d. At this point i thought i had the problem solved ... the ratio of d to a was 3 (lol). Well, maybe not lol yet, i still don't get what i'm doing wrong B) my traditional understanding of ratios is as follows, if a = 3d then to me that means for every A there are 3 d's. based on this, i set up the ration of a to d as 1:3. from here, i made the assumption that if a to d was 1:3 then d to a was 3:1here's the dilemma ... i know the answer is 1/3 ... however, even though i see why this is the case when i plug in the numbers (for example, i set A to 12 and get d=4, giving me a ratio of 4 to 12) i still don't get the theoretical explanation thanks for your help

Subhotosh Khan

USA
9117 Posts

 Posted - 05/03/2008 :  18:44:35 quote:Originally posted by Finesse4evai recently ran into a problem that made me question whether i understand ratios as well as i think i do ... The question states If a = 2b, 1/2b=c, and 4c = 3d then what is the ratio of d to a? a) 1/3b) 3/4c) 1d) 4/3e) 3 i set up the following ration of a = 2b = 4c = 3d. At this point i thought i had the problem solved ... the ratio of d to a was 3 (lol). Well, maybe not lol yet, i still don't get what i'm doing wrong B) my traditional understanding of ratios is as follows, if a = 3d then to me that means for every A there are 3 d's. based on this, i set up the ration of a to d as 1:3. from here, i made the assumption that if a to d was 1:3 then d to a was 3:1here's the dilemma ... i know the answer is 1/3 ... however, even though i see why this is the case when i plug in the numbers (for example, i set A to 12 and get d=4, giving me a ratio of 4 to 12) i still don't get the theoretical explanation thanks for your helpa = 2b, 1/2b=c, and 4c = 3dsuppose d = 4then c = 3then 2b = 1/3then a = 1/3then d/a = 12 not 1/3 as you had indicated the answer to beAre you sure you have posted the problem correctly?

Finesse4eva
Junior Member

USA
6 Posts

 Posted - 05/03/2008 :  19:07:12 hey subhotosh, yes, i posted the problem correctly. it's from a kaplan work book. i think you confused a with d/a. if d = 4, as you stated, then a = 12 (not d/a = 12) and da = 4/12 or 1/3as the original problem stated a = 2b ... 1/2b=c .... 4c =3d assume a = 12 .... then 12 = 2b and b = 6if b=6 .... then c = 3 and if c = 3 ... then 12 = 3d ... and d = 4so if a =12, and d = 4, d/a = 4/12like i said, i understand it when i put the numbers in, i just have trouble understanding the theory ahh! i just look back up the explanation you put up. i follow you up to c = 3 but 2b does not equal 1/3. if c = 3 then 1/2b = 3 ... b would equal 6 and 2b would therefore equal 12. suppose d = 4then c = 3then 2b = 1/3then a = 1/3

Subhotosh Khan

USA
9117 Posts

 Posted - 05/03/2008 :  21:29:37 If a = 2b, 1/2 * b=c, and 4c = 3d then what is the ratio of d to a? So thend/a = d/(2*b) = d/(4*c) = d/(3*d) = 1/3

Mrspi

USA
998 Posts

 Posted - 05/03/2008 :  21:31:00 quote:Originally posted by Finesse4evai recently ran into a problem that made me question whether i understand ratios as well as i think i do ... The question states If a = 2b, 1/2b=c, and 4c = 3d then what is the ratio of d to a? a) 1/3b) 3/4c) 1d) 4/3e) 3 i set up the following ration of a = 2b = 4c = 3d. At this point i thought i had the problem solved ... the ratio of d to a was 3 (lol). Well, maybe not lol yet, i still don't get what i'm doing wrong B) my traditional understanding of ratios is as follows, if a = 3d then to me that means for every A there are 3 d's. based on this, i set up the ration of a to d as 1:3. from here, i made the assumption that if a to d was 1:3 then d to a was 3:1here's the dilemma ... i know the answer is 1/3 ... however, even though i see why this is the case when i plug in the numbers (for example, i set A to 12 and get d=4, giving me a ratio of 4 to 12) i still don't get the theoretical explanation thanks for your helpI'm going to pretend that I didn't read any of the previous posts on this problem, and tell you how I would solve it, from the beginning.You are GIVEN that a = 2b.You are also told that1/2b = cSo, 1/a = cYou're also told that4c = 3dSubstitute (1/a) for c:4*(1/a) = 3d4/a = 3dYou are looking for the ratio of d to a, which in fraction form, is d/a....Now...can you take the equation 4/a = 3d and get it into the form where you have d/a on one side??This should not be too hard to do. If you are still having trouble with this problem, please repost and show us the work you've done.

peppers18

124 Posts

 Posted - 05/04/2008 :  01:31:47 mrspi, if 4/a=3d, then there is no way to get d/a=number. the best you could do is da=number.1/2b=c should be read as (1/2)b=cfinesse4eva: your equation ends up being a=3d. rearrange that so it says d/a=number. also, you are relating your equations and ratios incorrectly. a=3d says that a is 3 times as big as d. it does not tell you that for each a, there are 3 d's. use this relationship to find the ratio d:ad:a ==>d:3d ==>1:3so the ratio of d:a is 1:3

Finesse4eva
Junior Member

USA
6 Posts

 Posted - 05/08/2008 :  18:52:24 hey guys, thank for the comments. they were helpful. i figured it was a critical conception to nail down so i wouldn't let it go until i could figure out why theoretically d/a was 1/3. your techniques definitely help clarify some ambiguities... i think it finally made sense to me was i realize that 1/3 of one D was equal to one A ... once i realize that i saw why there was a ration of one D to three A's (1/3 * 3 : 1*3 = 1:3). once again, thank you for your insights... i about to post 2 problems so hopefully you can chime in on those problems as well
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