Answer:
The augmented matrix is:
[tex]\left[\begin{array}{cccc}1&1&1&15\\-1&1&0&2\\3&5&7&77\end{array}\right][/tex]
Step-by-step explanation:
Ntice there are three unknowns:
Number of small bags sold , let's name it S
Number of medium bags sold , let's name this M
Number of large bags sold, let's name this L.
We need now to start by writing the three equations that relate these three unknowns
1) Total number of bags sold: 15
S + M + L = 15 equation (1)
2) Two more medium bags were sold than small bags
M = 2 + S which can also be written as: M - S = 2 equation (2)
(grouping all unknowns on the left and pure numerical on the right of the equal sign)
3) The total sales is $77, so we create a value equation using the value of each item times the nunber of those sold:
3 S + 5 M + 7 L = 77 equation (3)
Now we write the augmented matrix for these three equations using the first column for the variable S (number of small bags), the second colum for the variable M (number of medium bags), the third column for L (number of large bags), and the 4th column for the strictly numerical terms that we located on the right hand side of the equal signs in all three equations:
[tex]\left[\begin{array}{cccc}1&1&1&15\\-1&1&0&2\\3&5&7&77\end{array}\right][/tex]
The solving of this augmented matrix via RREF calculations results in:
S = 4, M = 6, and L = 5
