SOLUTION: A mixture contains alcohol and water in the ratio of 12:5. On adding 14litres of water, the ratio of alcohol to water becomes 4:3. The quantity of alcohol in the mixture is?

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Question 986562: A mixture contains alcohol and water in the ratio of 12:5. On adding 14litres of water, the ratio of alcohol to water becomes 4:3. The quantity of alcohol in the mixture is?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
alcohol:water
12:5

Fourteen liters of water added, making 4:3.

Initial blend is 5%2F%2812%2B5%29=5%2F17 in water.
New blend becomes 3%2F7 in water. Also 4%2F7 in alcohol.

h, how much initial alcohol
w, how much initial water
Ration initially h:w
h%2Fw=12%2F5

New fraction blend as alcohol, 4%2F7;
h%2812%2F17%29%2F%28h%2Bw%2B14%29=4%2F7
The water adds to the amount of blend, but does not add to the fraction of alcohol.

Use the initial ratio solved for w, and substitute into the new blend alcohol equation.
w%2Fh=5%2F12
w=h%285%2F12%29
-
highlight_green%28h%2812%2F17%29%2F%28h%2B%285%2F12%29h%2B14%29=4%2F7%29
Solve this equation for h.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A mixture contains alcohol and water in the ratio of 12:5. On adding 14litres of water, the ratio of alcohol to water becomes 4:3. The quantity of alcohol in the mixture is?
The equation to solve is: 12x%2F%285x+%2B+14%29+=+4%2F3

After solving for x, multiply that value by 12 to get amount of alcohol



You should get: highlight_green%2842L%29 of alcohol