Question 914456
5 rings, 16 grams each ----> 5*16 = 80 grams total


10% silver: 80*0.10 = 8 grams of pure silver
90% gold: 80*0.90 = 72 grams of pure gold


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We have 72 grams of pure gold out of 80 grams of alloy (silver + gold)


Currently, the fraction is 72/80. This leads to 9/10 = 90% gold


Now add x grams of pure silver. We do NOT add this to the 72 since that represents all gold. We add this to the 80 since that represents silver+gold.



So we have this fraction now: {{{72/(80+x)}}}


So the model is {{{G(x) = 72/(80+x)}}}


We want the gold fraction to be equal to 80/100 (ie 80%), so {{{g(x) = 80/100}}} and {{{72/(80+x) = 80/100}}}




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Solve for x


{{{72/(80+x) = 80/100}}}


{{{72/(80+x) = 4/5}}}


{{{72*5 = 4(80+x)}}}


{{{360 = 320+4x}}}


{{{360 - 320=4x}}}


{{{40=4x}}}


{{{40/4=x}}}


{{{10=x}}}


{{{x=10}}}


You need to add <font size=5 color="red">10 grams</font> of pure silver to get an 80% gold alloy.



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Thanks,


Jim