Problema Solution
An 18 gram sample of a metal alloy composed of silver (at 10% concentration)
and gold (at 90% concentration) will be be melted into a liquid. Pure silver will then be added
to lower the concentration of gold.
a.Find a model for the gold concentration C, in terms of the amount of silver s (in grams)
added to the alloy.
b. How much pure silver should be added to this sample to lower the gold concentration to
75%?
Answer provided by our tutors
let
s = grams of 100% silver and 0% gold (pure silver) that needs to be added
18 grams sample has 0.10*18 = 1.8 grams silver and 0.90*18 = 16.2 grams gold
a. let C(x) is the gold concentration after s grams of silver are added to the alloy
the % of gold of the 18 g sample + 0% gold of s grams pure silver = C(s)/100 % of the new alloy
0.90*18 + 0*s = (C(s)/100)*(18 + s)
C(s) = 1620/(s + 18)% in the concentration of gold in the new alloy
b. s = ? so that C(s) = 75
1620/(s + 18) = 75
s = 1620/75 - 18
s = 3.6 g
3.6 grams pure silver should be added.