Question

See attached. Please Help

Answer 1

Let A = ounces of Type A
Let B = ounces of Type B
Let C = ounces of Type C

Set up a system of three equations with three unknowns.

2A + 3B + C = 19 (Niacin)
3A + B + 3C = 29 (Thiamin)
7A + 5B + 8C = 78 (Riboflavin)

Answer 2

so what did you get using the three equations?

Answer 3

are the answers 19,29, and 78

Answer 4

No. You have to solve for A, B, and C.

Answer 5

I'm still working through it.

Answer 6

will you let me know when u get it

Answer 7

I am fixing my answers. I made a small computation error.

Answer 8

A = 4 ounces
B = 2 ounces
C = 5 ounces

Answer 9

You can also do it by using matrices:
\[\left[\begin{matrix}2 & 3 & 1 \\ 3 & 1 & 3 \\ 7 & 5 & 8\end{matrix}\right]\]
Where the first row is Niacin, 2nd= Thiamin ·d= Riboflavin, and the columns are type A,B,C respectively.
You set that equal to the quantities you want:
\[\left[\begin{matrix}2 & 3 & 1 \\ 3 & 1 & 3 \\ 7 & 5 & 8\end{matrix}\right]\left[\begin{matrix}A \\ B\\ C \end{matrix}\right]=\left[\begin{matrix}19 \\ 29\\ 78\end{matrix}\right]\]
Then you find the inverse of the 1st matrix and multiply by the other:
\[\left[\begin{matrix}A \\ B\\ C \end{matrix}\right]=\left[\begin{matrix}2 & 3 & 1 \\ 3 & 1 & 3 \\ 7 & 5 & 8\end{matrix}\right]^{-1}\left[\begin{matrix}19 \\ 29\\ 78\end{matrix}\right]\]
Finally, you get:
\[\left[\begin{matrix}A \\ B\\ C \end{matrix}\right]=\left[\begin{matrix}4 \\ 2\\ 5\end{matrix}\right]\]

P.S. I know mkuehn10 already solved it but I was halfway through when he did and I didn't just wan't to throw that work away...