## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$\text{Powder 1 = 30 mg, and Powder 2 = 15 mg}$
Let us consider that $\text{Powder 1 = x mg, and Powder 2 = y mg}$ Here, we have: $\text{Powder 1 contains 20% vitamin$B_{12}$and 30% vitamin E and} \\ \text{Powder 2 contains 40% vitamin$B_{12}$and 20% vitamin E}$ We set the two equations as follows: $0.2 x+0.4y=12~~~~~~~(1)$ $0.3x+0.2y = 12~~~~~~~(2)$ We multiply equation (1) by $\dfrac{3}{2}$ and then subtract it from equation (2) to obtain: $-0.4 y = -6 \implies y=15 \ mg$ Now, back-substitute the value of $y$ into Equation (1) to solve for $x$ $0.2 x+(0.4)(15)=12 \implies x=30 \ mg$ Therefore, our desired results are: $\text{Powder 1 = 30 mg, and Powder 2 = 15 mg}$