SOLUTION: A quantity of 50%silver alloy is melted together with a quantity of 70%silver alloy to produce 500g of alloy containing 65% silver.How much of each alloy was used?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A quantity of 50%silver alloy is melted together with a quantity of 70%silver alloy to produce 500g of alloy containing 65% silver.How much of each alloy was used?      Log On


   



Question 715788: A quantity of 50%silver alloy is melted together with a quantity of 70%silver alloy to produce 500g of alloy containing 65% silver.How much of each alloy was used?
Answer by josmiceli(19441) About Me  (Show Source):
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Let +a+ = grams of 50% alloy used
Let +b+ = grams of 70% alloy used
+.5a+ = grams of silver in 50% alloy
+.7b+ = grams of silver in 70% alloy
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(1) +%28+.5a+%2B+.7b+%29+%2F+500+=+.65+
(2) +a+%2B+b+=+500+
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(1) +.5a+%2B+.7b+=+.65%2A500+
(1) +.5a+%2B+.7b+=+325+
(1) +5a+%2B+7b+=+3250+
Multiply both sides of (2) by +5+
and subtract from (1)
(1) +5a+%2B+7b+=+3250+
(2) +-5a+-+5b+=+-2500+
+2b+=+750+
+b+=+375+
and, from (2)
(2) +a+%2B+375+=+500+
(2) +a+=+125+
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125 grams of 50% alloy was used
375 grams of 70% alloy was used
check:
(1) +%28+.5a+%2B+.7b+%29+%2F+500+=+.65+
(1) +%28+.5%2A125+%2B+.7%2A375+%29+%2F+500+=+.65+
(1) +%28+62.5+%2B+262.5+%29+%2F+500+=+.65+
(1) +325+%2F+500+=+.65+
(1) +325+=+325+
OK