SOLUTION: I have always struggled with word problems and college word problems aren't any better, so could you please help me with these problems. How much pure water must be mixed with 4

Question 423870: I have always struggled with word problems and college word problems aren't any better, so could you please help me with these problems.
How much pure water must be mixed with 4 pints of 50% developer to produce a mixture that is 39% developer?
A researcher orders a broth of 8% glucose for her lab. However, she needs a stronger broth, one that is 14.1% glucose. Fortunately, she has 70.6 liters of 41% glucose broth in the stock room. How much 14.1% glucose broth can she make?
Found 2 solutions by Alan3354, htmentor:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
How much pure water must be mixed with 4 pints of 50% developer to produce a mixture that is 39% developer?
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How much pure water must be mixed with 4 pints of 50% developer to produce a mixture that is 39% developer?
4 pts of 50% contain 2 pts of developer and 2 pts of water.
If that 2 pts of developer is 39%,
2 pt = 0.39S (S = total solution)
S = 2/0.39 =~ 5.128 pts
5.128 - 4 = 1.128 pts of water to add
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I'll do the other one later, or you can repost it.
Posting more than one problem at a time usually results in waiting longer for help, btw.

Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
1. If we start with 4 pints of 50% developer, this means that we initially have equal parts developer and water, i.e. 2 pints of each. To dilute the mixture to 39%, how many pints of water do we need to add?
The initial ratio = 0.5 = 2 pints developer/4 pints solution
Final ratio = 0.39 = 2 pints developer/(4 + x) pints solution
Solve for x: 0.39(4 + x) = 2 -> 1.56 + 0.39x = 2 -> 1.128 pints water added
To help visualize this, imagine if we wanted to dilute from 50% to 25%, then we would need to add 4 pints of water. This gives 2 pints of developer in 8 pints of solution for a ratio of 0.25.
2. If we start with 70.6 liters of 41% glucose solution, this means we have 0.41*70.6 = 28.946 liters of glucose. How much 14.1% solution can we make?
Ratio = 0.141 = 28.946/x
Solving for x gives x = 28.946/0.141 = 205.291 liters.

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