|
|
|
Note: You must be registered in order to post a reply.
To register, click here. Registration is FREE!
|
| 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 d a = 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? |
|
|
| Math Forums @ Math Goodies |
© 2000-2004 Snitz Communications |
 |
|
|
Interactive Math Goodies Software
