an herbalist is making a medicinal blend of herbs. the blend includes ground ginseng, which costs $33.85 per…

an herbalist is making a medicinal blend of herbs. the blend includes ground ginseng, which costs $33.85 per kilogram, and golden chia, which costs $16.25 per kilogram. overall, the blend costs $25.05 per kilogram. if the herbalist already has 2 kilograms of ginseng prepared, how many kilograms of golden chia should she add? write your answer as a whole number or as a decimal rounded to the nearest tenth. kilograms

an herbalist is making a medicinal blend of herbs. the blend includes ground ginseng, which costs $33.85 per kilogram, and golden chia, which costs $16.25 per kilogram. overall, the blend costs $25.05 per kilogram. if the herbalist already has 2 kilograms of ginseng prepared, how many kilograms of golden chia should she add? write your answer as a whole number or as a decimal rounded to the nearest tenth. kilograms

Answer

Answer:

2.5

Explanation:

Step1: Set up the cost - equation

Let $x$ be the number of kilograms of golden chia. The cost of the ginseng is $33.85\times2$ dollars, the cost of the golden chia is $16.25x$ dollars, and the total mass of the blend is $(2 + x)$ kilograms with a cost of $25.05(2 + x)$ dollars. So, $33.85\times2+16.25x=25.05(2 + x)$.

Step2: Expand the right - hand side

$67.7+16.25x = 50.1+25.05x$.

Step3: Move the $x$ terms to one side

$25.05x-16.25x=67.7 - 50.1$.

Step4: Simplify both sides

$8.8x=17.6$.

Step5: Solve for $x$

$x=\frac{17.6}{8.8}=2.5$.