Answer:
15lb chicken 30 oz. soy sauce 5lb. green peppers
2 1/2 lb. scallions 10 oz. ginger
10 cups Water
False because multiple inputs can’t have the same output
The correct equation that models for this problem is x over y or x/y.
Let the following values be:
x - would be the money or commissions that Duncan earned.
y - would be the 20 percent that he gives his assistant
![\huge \boxed{\mathbb{QUESTION} \downarrow}](https://tex.z-dn.net/?f=%20%5Chuge%20%5Cboxed%7B%5Cmathbb%7BQUESTION%7D%20%5Cdownarrow%7D)
![\begin{bmatrix} \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \end{bmatrix} \begin{bmatrix} \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { - 1 } & { 1 } & { 5 } \end{array} \end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D%20%5Cbegin%7Barray%7D%20%7B%20l%20l%20%7D%20%7B%202%20%7D%20%26%20%7B%203%20%7D%20%5C%5C%20%7B%205%20%7D%20%26%20%7B%204%20%7D%20%5Cend%7Barray%7D%20%5Cend%7Bbmatrix%7D%20%5Cbegin%7Bbmatrix%7D%20%5Cbegin%7Barray%7D%20%7B%20l%20l%20l%20%7D%20%7B%202%20%7D%20%26%20%7B%200%20%7D%20%26%20%7B%203%20%7D%20%5C%5C%20%7B%20-%201%20%7D%20%26%20%7B%201%20%7D%20%26%20%7B%205%20%7D%20%5Cend%7Barray%7D%20%5Cend%7Bbmatrix%7D)
![\large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}](https://tex.z-dn.net/?f=%20%5Clarge%20%5Cboxed%7B%5Cmathbb%7BANSWER%5C%3A%20WITH%5C%3A%20EXPLANATION%7D%20%5Cdownarrow%7D)
![\begin{bmatrix} \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \end{bmatrix} \begin{bmatrix} \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { - 1 } & { 1 } & { 5 } \end{array} \end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D%20%5Cbegin%7Barray%7D%20%7B%20l%20l%20%7D%20%7B%202%20%7D%20%26%20%7B%203%20%7D%20%5C%5C%20%7B%205%20%7D%20%26%20%7B%204%20%7D%20%5Cend%7Barray%7D%20%5Cend%7Bbmatrix%7D%20%5Cbegin%7Bbmatrix%7D%20%5Cbegin%7Barray%7D%20%7B%20l%20l%20l%20%7D%20%7B%202%20%7D%20%26%20%7B%200%20%7D%20%26%20%7B%203%20%7D%20%5C%5C%20%7B%20-%201%20%7D%20%26%20%7B%201%20%7D%20%26%20%7B%205%20%7D%20%5Cend%7Barray%7D%20%5Cend%7Bbmatrix%7D)
In matrix multiplication, the number of columns in the 1st matrix is equal to the number of rows in the 2nd matrix.
![\left(\begin{matrix}2&3\\5&4\end{matrix}\right)\left(\begin{matrix}2&0&3\\-1&1&5\end{matrix}\right)](https://tex.z-dn.net/?f=%5Cleft%28%5Cbegin%7Bmatrix%7D2%263%5C%5C5%264%5Cend%7Bmatrix%7D%5Cright%29%5Cleft%28%5Cbegin%7Bmatrix%7D2%260%263%5C%5C-1%261%265%5Cend%7Bmatrix%7D%5Cright%29%20)
Multiply each element of the 1st row of the 1st matrix by the corresponding element of the 1st column of the 2nd matrix. Then add these products to obtain the element in the 1st row, 1st column of the product matrix.
![\left(\begin{matrix}2\times 2+3\left(-1\right)&&\\&&\end{matrix}\right)](https://tex.z-dn.net/?f=%5Cleft%28%5Cbegin%7Bmatrix%7D2%5Ctimes%202%2B3%5Cleft%28-1%5Cright%29%26%26%5C%5C%26%26%5Cend%7Bmatrix%7D%5Cright%29%20)
The remaining elements of the product matrix are found in the same way.
![\left(\begin{matrix}2\times 2+3\left(-1\right)&3&2\times 3+3\times 5\\5\times 2+4\left(-1\right)&4&5\times 3+4\times 5\end{matrix}\right)](https://tex.z-dn.net/?f=%5Cleft%28%5Cbegin%7Bmatrix%7D2%5Ctimes%202%2B3%5Cleft%28-1%5Cright%29%263%262%5Ctimes%203%2B3%5Ctimes%205%5C%5C5%5Ctimes%202%2B4%5Cleft%28-1%5Cright%29%264%265%5Ctimes%203%2B4%5Ctimes%205%5Cend%7Bmatrix%7D%5Cright%29%20)
Simplify each element by multiplying the individual terms.
![\left(\begin{matrix}4-3&3&6+15\\10-4&4&15+20\end{matrix}\right)](https://tex.z-dn.net/?f=%5Cleft%28%5Cbegin%7Bmatrix%7D4-3%263%266%2B15%5C%5C10-4%264%2615%2B20%5Cend%7Bmatrix%7D%5Cright%29%20)
Now, sum each element of the matrix.
![\large\boxed{\boxed{\left(\begin{matrix}1&3&21\\6&4&35\end{matrix}\right) }}](https://tex.z-dn.net/?f=%20%5Clarge%5Cboxed%7B%5Cboxed%7B%5Cleft%28%5Cbegin%7Bmatrix%7D1%263%2621%5C%5C6%264%2635%5Cend%7Bmatrix%7D%5Cright%29%20%7D%7D)