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

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.

18/75 = .24 * 100 = 24%.

that's your solution.

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