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Answer on Algebra Question for rain

Question #23413
A machine holds 14 quarts of coolant. Some of the coolant is inside the machine and some is contained in the radiator.
This radiator holds 4 quarts of coolant. The only way to add fresh coolant is to drain and refill the radiator.
If you completely drain the container and refill it with fresh coolant 3 times, how much of the old coolant still remains?
After each drain and refill, you run the machine to allow the new and old coolant to thoroughly mix together. (Hint: Work
with ratios)
Expert's answer
After the first time:
fresh coolant: 4 quarts
old coolant: 14-4 = 10 quarts.
After the second time:
fresh coolant: 4+10*(4/14)= 4(1+10/14) = 4*24/14=48/7 quarts
old coolant: 14 - 48/7 = 50/7 quarts
After the third time:
fresh coolant: 4+10*([48/7]/[(50+48)/7]) = 4+10*48/98 = 4(1+10*12/98) = 436/49 quarts
old coolant: 14 - 436/49 = 250/49 quarts
Answer:& 250/49 quarts

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