SOLUTION: A jeweler has 5 rings, each weighing 12 g, made of an alloy of 5% silver and 95% gold. She decides to melt down the rings and add enough silver to reduce the gold content to 76%. H
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Question 992178: A jeweler has 5 rings, each weighing 12 g, made of an alloy of 5% silver and 95% gold. She decides to melt down the rings and add enough silver to reduce the gold content to 76%. How much silver should she add? Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! assuming the distribution is by weight, then you have 3 grams of silver and 57 grams of gold in a total of 60 grams of rings.
that's because .05 * 60 = 3 and .95 * 60 = 57.
you have a total of 60 grams because 5 rings at 12 grams apiece makes 5 * 12 = 60 grams total.
you want to add x number of grams of silver to this total to make the total percent of silver equal to 24%.
we got the 24% silver by subtracting 76% of gold from 100% total to get 24% of silver.
the formula to use would be:
3 + x = .24 * (60 + x)
simplify to get 3 + x = 14.4 + .24 * x
subtract .24 * x from both sides of the equation and subtract 3 from both sides of the equation to get:
x - .24 * x = 14.4 - 3
simplify to get:
.76 * x = 11.4
divide both sides of the equation by .76 to get:
x = 11.4 / .76 = 15.
she needs to add 15 grams of silver to the mix.
3 grams of silver plus 15 grams of silver = 18 grams of silver.
60 total grams plus 15 grams of silver = 75 total grams.
