SOLUTION: A silversmith wishes to obtain an alloy containing at least 72% silver and at most 75% silver. Determine the greatest and least amounts of an 80% silver alloy that should be combin
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Question 995434: A silversmith wishes to obtain an alloy containing at least 72% silver and at most 75% silver. Determine the greatest and least amounts of an 80% silver alloy that should be combined with a 65% silver alloy in order to have 30grams of the required alloy. Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! This is 2 problems in 1
Let = grams of 80% alloy needed
Let = grams of 65% alloy needed
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First solve for 72% silver end result
(1)
(2)
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(2)
(2)
(2)
(2)
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Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)
-----------------------
and
(1)
(1)
-----------------------
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Now solve for 75% alloy end result
(1)
(2)
-----------------------------
(2)
(2)
(2)
(2)
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Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)
------------------------
and
(1)
(1)
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From these results,
the least amount of 80% alloy needed is 14 grams ( making 72% silver )
the most amount of 80% alloy needed is 20 grams ( making 75% silver )
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You can check the answers by plugging and back into (2) for both
72% and 75% cases
