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?
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Let x = fractional amt of antifreeze after 2 qts leak out & 2 qt water added
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Week 1:
{{{1/2}}}(16-2) = 16x (2 qts of water added to make it 16 again)
{{{1/2}}}(14) = 16x
7 = 16x
x = {{{7/16}}}; 
Therefore: {{{7/16}}}*16 = 7 qts, of antifreeze after week 1
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Week 2;
{{{7/16}}}(16-2) = 16x
{{{7/16}}}14 = 16x
{{{98/16}}} = 16x
x = {{{98/16}}}*{{{1/16}}}
x = {{{98/256}}}; 
Therefore: {{{98/256}}}*16 = 6.125 qts of antifreeze after week 2
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Week 3:
{{{98/256}}}(16-2) = 16x
{{{98/256}}}(14) = 16x
{{{1372/256}}} = 16x
x = {{{1372/256}}} * {{{1/16}}}
x = {{{1372/4096}}}; 
therefore: {{{1372/4096}}}*16 = 5.34 qts of antifreeze after week 3
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Hope this makes sense.