document.write( "Question 113028: i have no idea how to solve this, can someone please help me? a silversmith has two alloys. the first alloy is 28% silver and the second is 60% silver. how many grams of each should be mixed to produce 80 grams of an alloy that is 52% silver? So i should have came up with 2 answers right? stumped! \n" ); document.write( "

Algebra.Com's Answer #82326 by Earlsdon(6294) $\"\"$ $\"About$

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Let x = the number of grams of 28% Ag alloy. (Note: Ag = chemical symbol for silver)
\n" ); document.write( "and (80-x) = the number of grams of 60% Ag alloy.
\n" ); document.write( "The sum of these two amounts equals the 80 grams of 52% Ag alloy.
\n" ); document.write( "Basically, we will add the amounts of silver in the two alloys to come up with the amount of silver in the 80 grams of silver alloy.
\n" ); document.write( "The amount of silver in the x grams of the 28% Ag alloy can be written:
\n" ); document.write( "x(0.28)
\n" ); document.write( "The amount of silver in the (80-x) grams of 60% Ag alloy can be written:
\n" ); document.write( "(80-x)(0.6), so if we add these two we should get 80 grams of 52% Ag alloy which contains 80(0.52) grams of silver.
\n" ); document.write( "x(0.28)+(80-x)(0.6) = 80(0.52) Simplify and solve for x.
\n" ); document.write( "0.28x + 48 - 0.6x = 41.6 Combine like-terms.
\n" ); document.write( "-0.32x = -6.4
\n" ); document.write( "x = 20 and (80-x) = 60
\n" ); document.write( "So, the silversmith would need 20 grams of the 28% Ag alloy and 60 grams of the 60% Ag alloy to obtain 80 grams of 52% Ag alloy.
\n" ); document.write( "Check: Add the number of grams of silver in the 28% Ag alloy to the number of grams of silver in the 60% Ag alloy to get the number of grams of silver in the 80 grams of 52% Ag alloy.
\n" ); document.write( "20(0.28)+60(0.6) = 5.6+36 = 41.6
\n" ); document.write( "80(0.52) = 41.6 \n" ); document.write( "

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