SOLUTION: Q.28 two vessels contain mixtures of milk and water in the ration 8:1 and 1:5 respectively. find how much be drawn from each vessel to fill a third vessel of of capacity 21 gallons

Question 943552: Q.28 two vessels contain mixtures of milk and water in the ration 8:1 and 1:5 respectively. find how much be drawn from each vessel to fill a third vessel of of capacity 21 gallons in order that the resulting mixture may be half milk and half water is-

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount that must be drawn from vessel (8:1)
Then 21-x=amount that must be drawn from vessel(1:5)
First vessel contains (8/9) milk and (1/9) water
Second vessel contains (1/6) milk and (5/6) water
Now we know that the amount of pure milk that exists before the mixture takes place ((8/9)*x+(1/6)(21-x)) has to equal the amount of pure milk that exists after the mixture takes place (1/2)*21. Sooooo:
(8/9)x+(21/6)-(1/6)x=21/2 multiply each term by 18
16x+63-3x=189
13x=126
x=9.69 gal-----amount needed from vessel(8:1)
21-x=21-9.69=11.31 gal----amount needed from vessel(1:5)
CK
(8/9)*(9.69)+(1/6)*(11.31)=(21/2)= 10.5
8.61+1.89=10.5
10.495~~~~~10.5 Close enough---roundoff error
Hope this helps---ptaylor

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