SOLUTION: : 1 jar contains 5/6 alcohol and another 8/9 alcohol . how many liters taken from each jar are required to fill a third jar with capacity of 24 liter so that the mixture will be se

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Question 769654: : 1 jar contains 5/6 alcohol and another 8/9 alcohol . how many liters taken from each jar are required to fill a third jar with capacity of 24 liter so that the mixture will be seven eighths.
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
1 jar contains 5/6 alcohol and another 8/9 alcohol . how many liters taken from each jar are required to fill a third jar with capacity of 24 liter so that the mixture will be seven eighths.
--------------
alc + alc = alc
(5/6)x + (8/9)(24-x) = (7/8)24
------
(5/6)x + (8/9)(24-x) = 21
------
Multiply thru by 18 to get:
15x + 16*24 - 16x = 18*21
----
-x = -6
x = 6 liters (amt to take from the (5/6) jar
24-x = 18 liters (amt to take from the (8/9) jar
==============
Cheers,
Stan H.
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
The other tutor used 1 unknown.  Here it is using 2. Word problems involving
multiply answers are usually easier to set up if you use multiple unknowns.

: 1 jar contains 5/6 alcohol and another 8/9 alcohol . how many liters taken from each jar are required to fill a third jar with capacity of 24 liter so that the mixture will be seven eighths.
Let the answer be

We take x liters out of the first jar and y liters out of the second jar,
so that x + y = 24 liters.

The amount of alcohol in the x liters is x [and the rest water].

The amount of alcohol in the y liters is y [and the rest water].

So the amount of alcohol in the third jar is x + y [and the
rest water].

The third jar contains 24 liters.

So also the amount of alcohol in the third jar is ·24 or 21 liters of
alcohol [and the rest water].

So we set the two expressions for the amount of alcohol in the third jar
equal, and we have

               x + y  = 21

So our system of equations is

               x + y  = 21
                          x + y = 24

Clear the first of fractions by multiplying it through by LCD of 18

               15x + 16y = 21
                   x + y = 24

Solve that system and get x = 6 and y = 18

Answer: Take 6 liters from the jar that contains ths alcohol and 
18 liters from the jar that contains ths alcohol.

Edwin
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