SOLUTION: how much pure antifreeze must be added to 12L of a 40% solution of antifreeze to obtain a 60% solution?
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-> SOLUTION: how much pure antifreeze must be added to 12L of a 40% solution of antifreeze to obtain a 60% solution?
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You can put this solution on YOUR website! In 12 Liters of a 40% solution of anti-freeze there are 4.8 liters of pure anti-freeze.
You get this by multiplying 0.4 times 12 liters.
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You are going to add an unknown amount of pure anti-freeze to that solution. Call this unknown
amount X. When you are done adding amount X, the total amount of anti-freeze in the solution
will be 4.8 + X liters.
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But when you add X liters of anti-freeze to the 12 liters of solution, the amount of solution
also increases by the amount of X. So when you are done adding amount X, the total amount of
solution will be 12 + X liters.
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You want the ratio of the amount of anti-freeze in the solution to the entire amount of
solution to be 60% or its decimal equivalent 0.6.
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So you want 4.8 + X divided by 12 + X to equal 0.6. In equation form this is:
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You can get rid of the denominator by multiplying both sides of the equation by (12 + X) as
follows:
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On the left side, the factor (12 + X) in the numerator cancels with the factor (12 + X) in
the denominator and you are left with:
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Multiply out the right side:
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Get rid of the 4.8 on the left side by subtracting 4.8 from both sides to get:
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and get rid of the 0.6*X on the right side by subtracting 0.6*X from both sides. The result is:
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Solve for X by dividing both sides of this equation by 0.4 and you get:
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So if you add 6 liters of pure anti-freeze to the 12 liters of 40% solution, you end up 18 liters
(the original 12 liters plus 6 more liters) of a 60% mixture.
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Check this through. The original 40% solution contained 4.8 liters of anti-freeze. You
added 6 liters of pure anti-freeze, so the new solution contains 10.8 liters of anti-freeze.
And there now 18 liters of the new solution. Does 10.8 liters divided by 18 liters equal
a 60% ratio? Your calculator will tell you that it does equal 0.6. So the answer checks.
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Hope this helps you to work this problem just by thinking about what you are doing when
you mix solutions.
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