SOLUTION: The radiator of a car holds 16 quarts of liquid of which 8 are antifreeze. The radiator has a leak and loses 2 quarts of liquid each week. Every week, 2 quarts of water are added.

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Question 161172: The radiator of a car holds 16 quarts of liquid of which 8 are antifreeze. The radiator has a leak and loses 2 quarts of liquid each week. Every week, 2 quarts of water are added. After 3 weeks how much antifreeze is left in the radiator? (explain your reasoning, just the answer is not sufficient).
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The radiator of a car holds 16 quarts of liquid of which 8 are antifreeze. The radiator has a leak and loses 2 quarts of liquid each week. Every week, 2 quarts of water are added. After 3 weeks how much antifreeze is left in the radiator?
:
Let x = fractional amt of antifreeze after 2 qts leak out & 2 qt water added
:
Week 1:
1%2F2(16-2) = 16x (2 qts of water added to make it 16 again)
1%2F2(14) = 16x
7 = 16x
x = 7%2F16;
Therefore: 7%2F16*16 = 7 qts, of antifreeze after week 1
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Week 2;
7%2F16(16-2) = 16x
7%2F1614 = 16x
98%2F16 = 16x
x = 98%2F16*1%2F16
x = 98%2F256;
Therefore: 98%2F256*16 = 6.125 qts of antifreeze after week 2
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Week 3:
98%2F256(16-2) = 16x
98%2F256(14) = 16x
1372%2F256 = 16x
x = 1372%2F256 * 1%2F16
x = 1372%2F4096;
therefore: 1372%2F4096*16 = 5.34 qts of antifreeze after week 3
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Hope this makes sense.