How many grams of gold should a coin of 30% gold be if when combined with a 10 gram pure gold necklace, it forms a metal that is 68% gold?

Question

How many grams of gold should a coin of 30% gold be if when combined with a 10 gram pure gold necklace, it forms a metal that is 68% gold?

Answer 1

.30x + 1.00(10) = .68(x+10)

x= amount of 30% needed

.3x +10 = .68x + 6.8

,68x -.3x = 10-6.8

.38x = 3.2

x= 3.2/.38

x = 320/38 = 160/19 = 8 8/19 grams of 30% gold mixed with 10 grams of pure gold to get 18 8/19 grams of 68% gold

if the goal had been exactly in between 100 and 30 = 65

equal amounts would be needed, 10 and 10 to get 20 of 65%

68 is very close to 65, so slightly less 30% is needed than 10 grams. 8 8/19 grams is slightly less than 10 grams

100-68=32

68-30 = 38

38/32 = 19/16=10/x

19x=160

x = 160/19 = 8 8/19

68% is slightly closer to 100% so you need slightly more of 100% than of 30% 10 grams is slightly more than 8 8/19 grams