Question 1170861
Gold is  {{{24/24}}} karats.


Quantity of the 18kt to use,  Q
Quantity of the 10kt to use, 200-Q
Wanted 200 grams of 16kt gold


{{{(18/24)Q+(10/24)(200-Q)=(16/24)*200}}}
Simplify and solve.


Multiply both sides by 24:
{{{18Q+10(200-Q)=16*200}}}


Divide both sides by 2:
{{{9Q+5(200-Q)=16*100}}}


{{{9Q+1000-5Q=1600}}}

{{{4Q=600}}}

{{{highlight(Q=150)}}}---------grams of the 18kt  material.

That means {{{highlight(50)}}} grams of the 10 kt material.