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 problem with understanding ratios

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T O P I C    R E V I E W
Finesse4eva 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) 1/3
b) 3/4
c) 1
d) 4/3
e) 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 3:1

here'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


6   L A T E S T    R E P L I E S    (Newest First)
Finesse4eva 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
peppers18 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=c





finesse4eva: 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:a

d:a ==>
d:3d ==>
1:3

so the ratio of d:a is 1:3
Mrspi Posted - 05/03/2008 : 21:31:00
quote:
Originally posted by Finesse4eva

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) 1/3
b) 3/4
c) 1
d) 4/3
e) 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 3:1

here'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






I'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 that

1/2b = c

So,

1/a = c


You're also told that

4c = 3d

Substitute (1/a) for c:

4*(1/a) = 3d

4/a = 3d

You 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.


Subhotosh Khan 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 then

d/a = d/(2*b) = d/(4*c) = d/(3*d) = 1/3

Finesse4eva 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 1/3

as the original problem stated

a = 2b ... 1/2b=c .... 4c =3d

assume a = 12 .... then 12 = 2b and b = 6

if b=6 .... then c = 3

and if c = 3 ... then 12 = 3d ... and d = 4

so if a =12, and d = 4, d/a = 4/12

like 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 = 4

then c = 3

then 2b = 1/3

then a = 1/3



Subhotosh Khan Posted - 05/03/2008 : 18:44:35
quote:
Originally posted by Finesse4eva

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) 1/3
b) 3/4
c) 1
d) 4/3
e) 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 3:1

here'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


a = 2b, 1/2b=c, and 4c = 3d

suppose d = 4

then c = 3

then 2b = 1/3

then a = 1/3

then d/a = 12 not 1/3 as you had indicated the answer to be

Are you sure you have posted the problem correctly?

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