Answer
200 grams of A,
40 grams of B
Work Step by Step
Let's say she uses x grams of food A
and y grams of food B.
Then,
total niacin:
0.12x+0.20y=32$\quad /\times 100$
$12x+20y=3,200$
and total retinol:
100x+50y=22,000.
We have a system
$\left\{\begin{array}{ll}
12x+20y=3,200 & /\times-5\\
100\mathrm{x}+50\mathrm{y}=22,000 & /2
\end{array}\right.$
(eliminates y)
$\left\{\begin{array}{ll}
-60x-100y=-16,000 & \\
200\mathrm{x}+100\mathrm{y}=44,000 & /add
\end{array}\right.$
$140x=28,000\quad/\div 140$
$x=\displaystyle \frac{28000}{140}=200$
Back-substitute:
$12x+20y=3,200$
$12(200)+20y=3,200$
$2400+20y=3200\quad/-2400$
$20y=800\quad/\div 20$
$y=\displaystyle \frac{800}{20}=40$
200 grams of A, 40 grams of B
