Answer:
[tex]Large => L=10[/tex]
[tex]Medium => M=20[/tex]
[tex]small => S=40[/tex]
Step-by-step explanation:
The number of small lemonades purchased is the number of mediums sold plus double the number of larges sold:
[tex]S=M+2L => S-M-2L = 0[/tex]
The total number of all sizes sold is 70:
[tex]S+M+L = 70[/tex]
One-and-a-half times the number of smalls purchased plus twice the number of mediums sold is 100:
[tex]1,5S+2M = 100[/tex]
The system of equations is:
[tex]S-M-2L = 0\\S+M+L = 70\\1,5S+2M = 100[/tex]
Matrix to solve by gauss-jordan elimination:
[tex]\left[\begin{array}{cccc}1&-1&-2&0\\1&1&1&70\\1.5&2&0&100\end{array}\right][/tex]
Solving from first row:
[tex]\left[\begin{array}{cccc}1&-1&-2&0\\0&2&3&70\\0&3.5&3&100\end{array}\right][/tex]
Solving from second row:
[tex]\left[\begin{array}{cccc}1&-1&-2&0\\0&2&3&70\\0&0&-4.5&-45\end{array}\right][/tex]
From this:
[tex]-4.5 L=-45 => L=10[/tex]
[tex]2 M+3*10=70 => M=20[/tex]
[tex]S -20-2*10=0 => S=40[/tex]
