Mixture problem

Question

most gold jewelry is 14-karat gold, approximately 58% gold. If 18-karat gold is 75% gold and 12-karat gold is 50% gold, how much of each should be used to make a 14-karat gold bracelet weighing 100 grams?

Answer 1

x = grams of 75% gold

y = grams of 50% gold

 

The given information translates into algebra as

 

(75%)x + (50%)y = (58%)(100 g) = 5800 g

x + y = 100 g

 

Solve this system of 2 linear equations in 2 unknowns x and y:

 

75x + 50y = 5800

x + y = 100

 

Answer:

 

x = 32 g

y = 68 g

 

Test the answer.

Answer 2

g represents the amount of 18 K

100 - g represents the amount of 12 K

0.75(g) + 0.50(100 - g) = 0.58(100)

 

Can you solve for g and answer?