Answer
The jeweler needs to combine 1kg $30\%$ gold and 3kg $10\%$ gold to create 4 kg of an alloy containing 15% gold.
Work Step by Step
Let x = Amount of $30\%$ gold
y = Amount of $10\%$ gold
From the given information we can make a system of equations:
$x+y=4$
$0.3x+0.1y=0.15.4$
The first equation could be: $y=4-x$
Use substitution since both equations have been solved for x.
$0.3x+0.1(4-x)=0.6$
$0.3x+0.4-0.1x=0.6$
$0.2x = 0.2$
$x=1$
Solve for y: $x+y=4$
$1+y=4$
$y=3$
The jeweler needs to combine 1kg $30\%$ gold and 3kg $10\%$ gold to create 4 kg of an alloy containing 15% gold.
