Question 992178
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.