Answer to Question #32394 in Algebra for Mark

Question

Gold is 19 times as heavy as water, copper is 9 times as heavy as water. in what ratio should these be mixed to get an alloy 15 times as heavy as water?

Answer 1

Suppose we have 1m^3 of water, 1m^3 of gold and 1m^3 of copper. Then we have for mass fractions 1 for water, 19 for gold and 9 for copper. We want to get 15 units of mass, so we need to get x m^3 of gold and 1-x m^3 of copper
19x+9(1-x)=15
19x+9-9x=15
10x=6
x=3/5
1-x=2/5
then we need to get 3 parts of gold and 2 parts of copper, so ratio is 3:2 gold to copper.