Question 549313: A machine holds 14 quarts of coolant. Some of the coolant is inside the machine and some is contained in an external container. This container holds 4 quarts of coolant. You can only drain and refill the coolant in this container. If you completely drain the container and refill it the fresh coolant three times how much old coolant will be left? After each refill you allow the old and new coolant to be mixed together.
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! After removal of 4 quarts, you have 10 quarts
of old coolant
Filling with 4 quarts of new coolant, you have
10 quarts old coolant, 4 quarts new coolant
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Now any coolant removed will have this ratio
new / old = 4/10
Removal of 4 quarts now means
4/( 4 + 10 ) x 4 = 16/14 quarts new removed
10/( 4 + 14 ) x 4 = 40/14 quarts old removed
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There is now 4 - (16/14) = 40/14 quarts new coolant left
There is now 10 - (40/14) = 100/14 quarts old coolant left
( notice this adds up to 10 quarts as it should )
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4 quarts of new coolant is added
Now the amount of new coolant is
( 56 + 40 )/14 = 96/14 quarts
The amount of old coolant is
100/14
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Now, any coolant removed will have this ratio,
new / old = 96 / 100
Removal of 4 quarts means
96/196 x 4 = 384/196 quarts new coolant removed
100/196 x 4 = 400/196 quarts old coolant removed
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96/14 - 384/196 = 960/196 quarts new coolant left
100/14 - 400/196 =1000/196 quarts old coolant left
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4 quarts of new coolant is added
Now the amount of new coolant is
( 784 + 960 )/196 = 1744/196 quarts
Amount of old coolant is
1000/196 quarts
there is 5.102 quarts of old coolant left
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check:
( 1744 + 1000 ) / 196 = 2744 / 196
2744 / 196 = 14
OK
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