SOLUTION: How water must Poison Ivy add to a 4 liter solution that contains 5% extract of baneberry to get a solution that contains 3% extract of baneberry?

Question 177685This question is from textbook College Algebra
: How water must Poison Ivy add to a 4 liter solution that contains 5% extract of baneberry to get a solution that contains 3% extract of baneberry? This question is from textbook College Algebra

Found 2 solutions by gonzo, Mathtut:
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
4 liters of 5% solution of poison ivy contains 95% water = .95*4 = 3.8 litres of water.
you want to know how much water must you add to make 3% solution of poison ivy.
a 3% solution of poison ivy would contain 97% water.
let x = amount of water you need to add.
your equation becomes:
(.95 * 4) + x = .97 * (x + 4)
this becomes:
3.8 + x = (.97 * x) + (.97 * 4)
this becomes:
3.8 + x = .97 * x + 3.88
subtract .97 * x from both sides and subtract 3.8 from both sides and the equation becomes:
x - .97*x = 3.88 - 3.8
which becomes:
.03*x = .08
divide both sides by .03 and it becomes:
x = .08/.03 = 2.66666666666667
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you have to add 2.666666666667 liters of water to the original solution.
4 litres + 2.66666666667 = 6.666666666667
your new solution has a total of 6.6666666667 litres.
the amount of poison ivy in this new solution stayed the same (you didn't add any more).
that amound was .05 * 4 = .2 litres of poison ivy.
.2 / 6.6666666666667 = .03 * 100% = 3% poison ivy in the solution making it a 3% solution.
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Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
You can simplify this by remembering in this particular problem the amount of pure baneberry is constant.
:
.05(4)=.2 pure baneberry....so 1/5 of a liter is baneberry.
:
this will stay the same because your not adding any baneberry. Your adding water. This fact will remain true no matter how much water you add. what will change is the percentage of baneberry to the new mixture. It (the percentage) will obviously become smaller as more water is added .
therefore since we want 3% of the new mixture to be baneberry we take the amount of baneberry .2 and set it equal to 3% of the new mixture 4+x, where x is the amount of water added.
:
.05(4)=.03(4+x)
:
.2=.12+.03x
:
.03x=.08
:
liters
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