The number of grams of pure silver in x plus the number of grams of pure silver in y is equal to the number of grams of pure silver in the 500 grams.
Let x and y be the weights, in grams, of sterling silver, and of the 90% alloy to make the 500 grams at 91%.
Hence, x+y=500
Pure silver is given in percentage forms.
Hence, 92.5% (x) + 90% (y) =91% (500)
Substitute y by 500−x in the last equation to write
92.5% (x) + 90% (500−x) =91% (500)
Simplify and solve
92.5x+45000−90x=45500
x=200 grams.
Hence, 200 grams of Sterling Silver is needed to make the 91% alloy.
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