SOLUTION: The cooling system of a car has a capacity of 15 liters. If the system is currently filled with a mixture that is 20​% ​antifreeze, how much of this mixture should b

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Question 1055108:
The cooling system of a car has a capacity of 15 liters. If the system is currently filled with a mixture that is 20​% ​antifreeze, how much of this mixture should be drained and replaced with pure antifreeze so that the system is filled with a solution that is 50% ​antifreeze?
Found 3 solutions by ikleyn, josgarithmetic, MathTherapy:
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
The cooling system of a car has a capacity of 15 liters. If the system is currently filled with a mixture that is 20​% ​antifreeze,
how much of this mixture should be drained and replaced with pure antifreeze so that the system is filled with a solution that is
50% ​antifreeze?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

See the lesson
    - Word problems on mixtures for antifreeze solutions
in this site.

Very similar problem was solved there (Problem 4).
Consider it as a sample. Read it attentively.
Then solve your problem by substituting your data.


Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Mixture problems".


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
c for capacity, c=15.
p for current percent antifreeze in the system, p=20.
T for the target percent wanted as result in the system, T=50.
v for volume of current 20% antifreeze to remove and replace with 100% antifreeze to reach T; v is unknown.

How much actual antifreeze in the system now?
c%2A%28p%2F100%29

How much actual antifreeze if remove v?
c%28p%2F100%29-%28p%2F100%29v

How much actual antifreeze when replace with v of 100%?
c%28p%2F100%29-%28p%2F100%29v%2Bv

Total volume of result mixture will be kept the same, c. The target concentration T is wanted.
highlight%28%28c%28p%2F100%29-%28p%2F100%29v%2Bv%29%2Fc=T%2F100%29
Solve for v.

A lesson very much in this manner but maybe different variable names is here:
the radiator antifreeze drain & replace problem

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The cooling system of a car has a capacity of 15 liters. If the system is currently filled with a mixture that is 20​% ​antifreeze, how much of this mixture should be drained and replaced with pure antifreeze so that the system is filled with a solution that is 50% ​antifreeze?
The equation you need is a simple one.



Let the amount to be drained and replaced by 100% antifreeze be D

We then get the following equation: highlight_green%28highlight%28.2%2815+-+D%29+%2B+D+=+.5%2815%29%29%29

Solve for D, the amount to be drained and replaced.

It's that simple...nothing complex!!