Caleb C.

asked • 01/13/17

I really need help with this geometry problem!!!

 A      3
--- = ---
 B      4
 
 
1. 3b=?
 
2. b/a=?
 
3. a/(a+b)=?
 

1 Expert Answer

By:

Andrew M. answered • 01/13/17

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Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

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a/b = 3/4
 
a = 3
b = 4
 
3b = 12
 
b/a = 4/3
 
a/(a+b) = 3/(3+4) = 3/7
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Arthur D.

tutor
Hi Andrew, I was looking at this problem earlier and I had a different approach. A and B don't have to be 3 and 4.
A/B could be another fraction not in lowest terms such as 15/20. I was going to do the problem using the variables.
If you get a chance give me your thoughts on this approach. Thanks.
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01/13/17

Andrew M.

you're correct that a, b could be any numbers
that teduce to 3/4.  
 
a/b = 3/4
 
3b = 4a
 
b/a = 4/3
 
note: a = 3b/4 ... 
 
a/(a+b) =
(3/4)b/[(3/4)b + b] 
             = (3/4)b/[(7/4)b]
              = (3b/4)(4/7b)
              = 3/7
or
 
b = 4a/3 ....
 
a/(a+b) =
a/[a+4a/3] =
a/(7a/3) = 
a(3/7a) = 
3/7
 
Approaching it using the variables only changes
the answer "3b =  " from 12 to 4a
 
b/a is still 4/3
a/(a+b) still equals 3/7
 
 
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01/13/17

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