SOLUTION: Pure, or 24-karat,gold is very soft, so it is rarely used for jewellery. Most gold jewellery contains a mixture of gold and some cheaper metal(s) to make it harder. Suppose a jewel

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Pure, or 24-karat,gold is very soft, so it is rarely used for jewellery. Most gold jewellery contains a mixture of gold and some cheaper metal(s) to make it harder. Suppose a jewel      Log On


   

Question 1021999: Pure, or 24-karat,gold is very soft, so it is rarely used for jewellery. Most gold jewellery contains a mixture of gold and some cheaper metal(s) to make it harder. Suppose a jewellery maker has some 18-karat gold (75% pure) and 9-karat gold (37.5% pure), and they want to make a new piece of 15-karat gold (62.5% pure) with a mass of 150 grams. What mixture should they use?
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
You can do this all in karats if you want.

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

system%28x%2By=150%2C%28%2818%2F24%29x%2B%289%2F24%29y%29%2F150=15%2F24%29

Simplify the karats equation.
%286%2F8%29x%2B%283%2F8%29y=150%285%2F8%29
%282%2F8%29x%2B%281%2F8%29y=50%285%2F8%29
2x%2By=50%2A5

The simplified system to solve is system%28x%2By=150%2C2x%2By=250%29.