SOLUTION: How many liters of water should be added to a 30 liter mixture of milk And Water in the ratio of 7:3 so that the mixture has 40% water in it? Please explain the answer. Thanks.

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Question 475288: How many liters of water should be added to a 30 liter mixture of milk And Water in the ratio of 7:3 so that the mixture has 40% water in it?
Please explain the answer. Thanks.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = liters of water to be added to mixture
Let b = liters of milk in 30 liter mixture
Let c = liters of water in 30 liter mixture
given:
(1) +b+%2B+c++=+30+
(2) +b%2Fc+=+7%2F3+
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Multiply both sides of (2) by 3c
(2) +3b+=+7c+
(2) +b+=+%287%2F3%29%2Ac+
Substitute (2) into (1)
(1) +%287%2F3%29%2Ac+%2B+c+=+30+
(1) +7c+%2B+3c+=+90+
(1) +10c+=+90+%7D%7D%0D%0A%281%29+%7B%7B%7B+c+=+9+
and
(1) +b+%2B+c+=+30+
(1) +b+%2B+9+=+30+
(1) +b+=+21+
----------------
In words:
(liters of water in final mixture) / (total liters of final mixture) = 40%
+%28+a+%2B+9+%29+%2F+%28+a+%2B+30+%29+=+.4+
+a+%2B+9+=+.4%2A%28a+%2B+30%29+
+a+%2B+9+=+.4a+%2B+12+
+.6a+=+3+
+a+=+5+
5 liters of water need to be added to the 30 liter mixture