Answer
See the explanation
Work Step by Step
Food A $=$ $\frac{0.12 niacin}{gram} +\frac{100 retinol}{gram}$,
Food B $=$ $\frac{0.2 niacin}{gram}+\frac{50retinol}{gram}$.
let $a$ denote mass of Food A and $b$ denote mass of Food B.
Thus, For niacin.
-Mass of Food A $\times$ niacin per gram of Food A$=$Total niacin of Food A. $0.12a$,
-Mass of Food B $\times$ niacin per gram of Food B$=$Total niacin of Food B. $0.2b$,
Therefore, $0.12a+0.2b=32$.
For retinol,
-Mass of Food A $\times$ retinol per gram of Food A$=$Total retinol of Food A. $100a$
-Mass of Food B $\times$ retinol per gram of Food B$=$Total retinol of Food B. $50b$
Therefore, $100a+50b=22000$.
Thus,
$\begin{cases}
0.12a+0.2b=32\\
100a+50b=22000
\end{cases}$
Multiplying Equation 1 by -250 and adding it together.
$\begin{cases}
-30a-50b=-8000\\
100a+50b=22000\\
-- -- -- -- --\\
70a=14000
\end{cases}$
Therefore, $a=200$. Substituting back in $50b=2000, b=40$.
