How much pure gold should be melted with 15 g of 14 karat gold to reduce 18 karat gold

Question

A karat Is a measure of the purity of gold in an alloy. Pure gold measures 24 carrots. And aloe that measures X carats is X over 24 gold. For example 18 karat gold is 18/24 is equal to three over four gold.

Answer 1

100% * X + 15 g * 14/24 = (X+15)*18/24

 

X + 15*7/12 = 3/4*(X + 15)

 

X + 5*7/4 = 3/4(X+15)

 

X + 35/4 = 3/4X + 45/4

 

X = 3/4X + 45/4 - 35/4

 

X  = 3/4X + 10/4

 

X - 3/4X = 5/2

 

1/4X = 5/2

 

X = 5/2*4 = 10

 

CHECK:

 

10 + 15*14/24 = 10 + 8.75 = 18.75 = 3/4 x 25 = 3/4 * (10 + 15)

 

The answer is checked, verified, and proven to be correct.

Mix 10 grams of pure gold.