Answer
$\text{Liquid 1 = 50 mg, and Liquid 2 = 75 mg}$
$\text{50 mg contains 20% vitamin C and 30% vitamin D}
\\ \text{and 75 mg contains 40% vitamin C and 20% vitamin D}$
Work Step by Step
Let us consider that $\text{Liquid 1 = x mg, and Liquid 2 = y mg}$
Here, we have:
$\text{Liquid 1 contains 20% vitamin C and 30% vitamin D}
\\ \text {and Liquid 2 contains 40% vitamin C and 20% vitamin D}$
We are given the system of equations as follows:
$0.2 x+0.4y=40~~~~~~~(1)$
$0.3x+0.2y = 30~~~~~~~(2)$
We multiply equation (1) by $\dfrac{3}{2}$ and then subtract it from equation (2) obtain:
$-0.4 y = -30 \implies y=75 \ mg $
Now, back-substitute the value $y$ into Equation (1) to solve for $x$
$0.2 x+(0.4)(75)=40 \implies x=50 \ mg $
Therefore, our desired results are:
$\text{Liquid 1 = 50 mg, and Liquid 2 = 75 mg}$
$\text{50 mg contains 20% vitamin C and 30% vitamin D}
\\ \text{and 75 mg contains 40% vitamin C and 20% vitamin D}$
