SOLUTION: how many quarts of pure antifreeze must be added to 6 quarts of a 10% antifreeze solution to obtain a 30%antifreeze solution?

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Question 366163: how many quarts of pure antifreeze must be added to 6 quarts of a 10% antifreeze solution to obtain a 30%antifreeze solution?
Found 2 solutions by Fombitz, Earlsdon:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let A be the number of quarts of 100% antifreeze.
100A%2B10%286%29=30%28A%2B6%29
100A%2B60=30A%2B180
70A=120
highlight%28A=12%2F7%29quarts

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
First, think in terms of the amounts of antifreeze in this situation.
Let x = the number of quarts of pure antifreeze to be added.
How much antifreeze is there in the six quarts of 10% antifreeze solution?
6quarts(10%) = 0.6 quarts of antifreeze.
The final antifreeze solution will be 6+x quarts of 30% antifreeze.
So now we can write the necessary equation to solve for x.
x+0.1(6) = 0.3(x+6) Simplify and solve for x.
x+0.6 = 0.3x+1.8 Subtract 0.3x from both sides.
0.7x+0.6 = 1.8 Subtract 0.6 from both sides.
0.7x = 1.2 Finally, divide both sides by 0.7
x = 1.71429
So you'll need to add 1.71429 quarts of pure antifreeze to the 6 quarts of 10% antifreeze solution to obtain 7.71429 (6+1.71429) quarts of 30% antifreze solution.