SOLUTION: Can someone please help me out with the following. 1)Two bottles have capacities in the ratio 4 to 7. The smaller bottle holds 6 ounces more than half of the larger bottle. How

Question 48747: Can someone please help me out with the following.
1)Two bottles have capacities in the ratio 4 to 7. The smaller bottle holds 6 ounces more than half of the larger bottle. How many ounces will the smaller bottle hold?
a. 12
b. 24
c. 36
d. 48
2)Solve x + 12/x-8 =0 (solutions)
3)solve 5/x + 2 = 10/3x(solutions)
4)7/x + 2= 6/x-5 (solutions)
5)solve x-4/x-2 = x-2/x +2 + 1/x-2 (solutions)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
)Two bottles have capacities in the ratio 4 to 7. The smaller bottle holds 6 ounces more than half of the larger bottle. How many ounces will the smaller bottle hold?
--------------------
Larger bottle contents: x ounces
Smaller bottle contents: (x/2) +6 ounces
EQUATION:
smaller/larger = 4/7
4(larger) = 7(smaller)
4x = 7((x/2)+6)
4x= (7/2)x + 42
(1/2) x = 42
------------------------
x=84 ounces (amount in larger bottle)
(x/2)+6= 42+6=48 ounces (amount in smaller bottle)
----------------------------
2)Solve x + 12/(x-8) =0
Multiply thru by (x-8) to get:
x^2-8x+12=0
(x-6)(x-2)=0
x=6 or x=2
---------------
3)solve 5/x + 2 = 10/3x
Multiply thru by 2x to get:
15+6x=10
6x=-5
x=-5/6
---------------
4)7/(x+2)= 6/(x-5)
Multiply thru by (x+2)(x-5) to get:
7(x-5)= 6(x+2)
x=47
--------------
5)solve (x-4)/(x-2) = (x-2)/(x+2) + 1/(x-2)
(x-4)(x+2)= (x-2)^2+(x+2)
x^2-2x-8 = x^2-4x+4 + x+2
x=14
----------
Cheers,
Stan H.

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