SOLUTION: A mechanic has found that a car with a 16-quart radiator has 40% antifreeze mixture in the radiator. He has a 80% antifreeze solution. How much of the 40% solution would he have to

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Question 733612: A mechanic has found that a car with a 16-quart radiator has 40% antifreeze mixture in the radiator. He has a 80% antifreeze solution. How much of the 40% solution would he have to replace with the 80% solution to get the radiator up to 55% antifreeze solution? (You must set up an equation and solve to receive credit)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The radiator contains 16 quarts of solution that is too weak.
If the mechanic removes x quarts of the 40% solution in the radiator, the radiator will have 16-x quarts of solution, containing
%2816-x%29%2A0.4 quarts of antifreeze.
After that, the mechanic adds x quarts of 80% antifreeze solution, containing
0.8%2Ax quarts of antifreeze.
At the end, the radiator will again contain 16 quarts of solution:
16-x%2Bx=16, but the amount of antifreeze in the radiator will be
%2816-x%29%2A0.4%2B0.8x
For the solution to be 55% antifreeze, the amount of antifreeze in the radiator should be
16%2A0.55 quarts or 8.8 quarts
The equation we should use to calculate the x value needed is
%2816-x%29%2A0.4%2B0.8x=16%2A0.55 or %2816-x%29%2A0.4%2B0.8x=8.8
%2816-x%29%2A0.4%2B0.8x=8.8 --> 6.4-0.4x%2B0.8x=8.8 --> 6.4%2B0.4x=8.8 --> 0.4x=8.8-6.4 --> 0.4x=2.4 --> x=2.4%2F0.4 --> highlight%28x=6%29
The mechanic should remove 6 quarts of solution from the radiator and replace them with 6 quarts of 80% antifreeze solution.