SOLUTION: Hawaiiain punch is 10% fruit juice. How much water would you have to add to one gallon of hawaiiain punch to get a drink that is 6% fruit juice? my homework is 1 thru 41 odd

First I'll give you the answer and check it. Then I'll tell
you how I got it.  The reason I do it this way is to show
you that it takes the exact same thinking to check a word
problem, starting with the answer, as it does to set up the
equation, starting with x.  You'll see.

The answer: You would have to add  of a gallon of water.

Checking using the answer  gallon of water.

We have 1 gallon of Hawaiian punch to begin with.
10% of 1 gallon is  gallon of fruit juice.
Suppose we add  gallon of water.  We will then
have  or  gallons of liquid of
which  gallon is fruit juice, so

 equals 

because  =  =  = 

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Now if you understand that, we will now "check it" using  gallon:

"Checking" using  gallon of water.

We have 1 gallon of Hawaiian punch to begin with.
10% of 1 gallon is  gallon of fruit juice.
Suppose we add  gallon of water.  We will then
have  gallons of liquid of
which  gallon is fruit juice, so

 equals 

or

 = 

Multiply both sides by 

 = 

Multiply both sides by 10

 = 

Multiply both sides by 10

 = 

 = 

Subtract 6 from both sides:

 = 

Divide both sides by 6

 = 

Simplifying:

 = 

Edwin