SOLUTION: 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 Could please help me with the above problem Thanks

Algebra ->  Equations -> SOLUTION: 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 Could please help me with the above problem Thanks       Log On


   

Question 339832: 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
Could please help me with the above problem
Thanks

Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Are there supposed to be 2 equal signs? Let me know if this is a typo or not.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
If b and c are positive numbers and 1/b = b/c = c/8 then b+c = ?

---------------------------

1/b = b/c = c/8 

Multiply all three sides by 8bc

8c = 8b² = bc²

Dividing 8c = 8b² through by 8 gives

c = b² 

Dividing 8c = bc² through by c gives

8 = bc

So we have the system of equations:

c = b² 
8 = bc

Substituting b² for c in 8=bc

8 = b(b²)

8 = b³

2 = b

Substituting in 

c = b² = 2² = 4

So,

b + c = 2 + 4 = 6   

So the correct choice is b + c = 6, choice B

-----------------------
Check to see that

1/b = b/c = c/8

1/2 = 2/4 = 4/8

which is true. So it checks.   

Edwin