Problem E

Mixture of Three

Kanza is making and selling trail mix. She makes three different blends, each consisting of a mixture of cashews, dark chocolate, and almonds. All of these blends are sold at the same price of \(\$18\) per kg.

If she mixes cashews, dark chocolate, and almonds in the ratio of \(1:1:1\), by mass, then she makes a profit of \(20\%\).

If she mixes cashews, dark chocolate, and almonds in the ratio of \(3:2:1\), by mass, then she makes a profit of \(8\%\).

If she mixes cashews, dark chocolate, and almonds in the ratio of \(1:4:2\), by mass, then she makes a profit of \(26\%\).

What price, in dollars per kg, does Kanza pay for each of the cashews, dark chocolate, and almonds?

What percentage of a profit would she make if she mixes cashews, dark chocolate, and almonds in the ratio of \(2:3:4\), by mass?