Question 1021999
You can do this all in karats if you want.


x for the 18 k gold
y for the 9 k gold


{{{system(x+y=150,((18/24)x+(9/24)y)/150=15/24)}}}


Simplify the karats equation.
{{{(6/8)x+(3/8)y=150(5/8)}}}
{{{(2/8)x+(1/8)y=50(5/8)}}}
{{{2x+y=50*5}}}


The simplified system to solve is  {{{system(x+y=150,2x+y=250)}}}.