Question 1135500
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So far, you have received 3 responses showing similar yet different algebraic methods for solving the problem.<br>
Here is an alternative which, if you understand how to use it, gets you to the answer to a mixture problem like this much faster and with far less effort.<br>
You are starting with 40% grape juice and adding 10% grape juice; you want to stop when the mixture is 30% grape juice.<br>
30% is 1/3 of the way from 40% to 10%; that means 1/3 of the mixture must be what you are adding.<br>
So 1/3 of the mixture is the 10% grape juice you are adding; so 2/3 of the mixture is the 40% grape juice you started with.  That means the 10% and 40% juices need to be mixed in the ratio 1:2.<br>
Then since you used 10 gallons of the 40% juice, you need 5 gallons of the 10% juice.