Fractions - Help please...

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Fractions - Help please...

by smushkas » Wed Aug 08, 2007 5:54 am
Hey guys,
Can anyone explain this problem?

17. If b and c are positive numbers and [1/b] = [b/c] = [c/8], then b + c =
(A) 4
(B) 6
(C) 7
(D) 8
(E) 9

Correct answer is (B)
Thanks in advance for your attention!
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Answer

by gmatz » Wed Aug 08, 2007 6:55 am
1/B = B/C = C/8

1. If 1/B = C/8 then 8 = CB and B= 8/C
2. Plug B back into the equation B/C = C/8 and simplify to get C^3 = 64 If C^3 = 64 then C = 4
3. Plug C = 4 back into the equation B = 8/C. So B = 2
4. B + C = 4 + 2 = 6
Last edited by gmatz on Wed Aug 08, 2007 1:30 pm, edited 1 time in total.

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by tanyajoseph » Wed Aug 08, 2007 11:15 am
How do u dedude to C^3 = 64???#
I get c^2 = 64. Could you help please explain how exactly you worked through?

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Sorry Corrected Answer Above

by gmatz » Wed Aug 08, 2007 1:31 pm
In my haste I wrote the equation incorrectly. This answer should make sense now.

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by II » Sat Dec 29, 2007 7:53 am
tanyajoseph wrote:How do u dedude to C^3 = 64???#
I get c^2 = 64. Could you help please explain how exactly you worked through?
Hi there ...
what answer do you come to here ? If in your calculation you say you get c^2 = 64, then this gives c a value of 8.
So if you Plug C = 8 back into the equation B = 8/C. So B = 1.
Which means b+c = 9 ... which is answer E ... which is incorrect.

Here's how I worked out the solution:
Step 1:
1/b = c/8
cross multiply to get bc = 8
so b = 8/c

Step 2:
Lets look at b/c = c/8
Plug in the value of b into this equation: (8/c)/c = c/8
This can be simplified (by cross multiplication) to read: (8/c)*8 = c^2
This can be simplified further to read: (8/c * 8/1) = c^2
which => 64/c = c^2
so 64 = c^3
so c = 4 (the cube root of 64)

Step 3:
From step 1 we got b = 8/c.
Now we know that c=4 ... we can get b = 8/4 = 2
Or we can just plug the value of c into the orginal numbers from the question:
1/b = b/ c
=> 1/b = b/4
cross multiply to get: b^2 = 4 ... so b = 2

Hence the answer to the queston: b + c => 2 + 4 = 6

We can check the answer by plugging these values b=2, c=4 into the original values from the question:
1/b = b/c = c/8
1/2 = 2/4 = 4/8

Hope this makes sense !
Best.
II