Question

An herbalist is mixing an 8-kilogram batch of a medicinal blend. The blend, which costs$29.40 per kilogram to make, is made up of ground ginseng at $34.95 per kilogram andgolden chia at $16.45 per kilogram. How many kilograms of each should be used to make the8-kilogram batch?Write your answers as whole numbers or as decimals rounded to the nearest tenth.

Answer 1

Let x kg be ground ginseng and y kg be golden chia.

The equation for the variables x and y are,

`\begin{gathered} x+y=8 \\ x=8-y \end{gathered}`
`\begin{gathered} 34.95x+16.45y=29.40\cdot8 \\ 34.95x+16.45y=235.2 \end{gathered}`

Substitute 8 - y for x in the equation to the value of y.

`\begin{gathered} 34.95(8-y)+16.45y=235.2 \\ -34.95y+16.45y=235.2-279.6 \\ y=-(44.4)/(-18.5) \\ =2.4 \end{gathered}`

Substitute 2.4 for y in equation x = 8 -y to obtain the vaues of x.

`\begin{gathered} x=8-2.4 \\ =5.6 \end{gathered}`

So 5.6 kg of ground ginseng and 2.4 kg of golden chia.