Mixed exercises

Question

How much pure gold(24k) must be mixed with 60% gold to get20 g of 75% gold

Answer 1

Let P = amount of pure gold

Let S = amount of 60% gold

 

20 g total  ==>  P + S = 20  ==>  S = 20 - P

 

The final mixture is 20 g of 75% gold  ==>  it contains .75*20 = 15 g gold

 

The amount of gold in a mixture of P and S must be 15  ==>

 

1.00*P + 0.60*S = 15 

 

Substitute the value for S in to the 2nd equation  

 

1.00*P + 0.60*(20 - P) = 15

P + 12 - 0.6*P = 15

0.4*P = 3

P = 3/0.4 = 30/4 = 7.5 g

 

So S = 20 - 7.5 = 12.5 g

 

So use 7.5 g pure gold and 12.5 g 60% gold

 

Check:  1*(7.5) + 0.6*(12.5) = 7.5 + 7.5 = 15 g gold in mixture which is 75% of 20 g total