Respuesta :
Answer:
Mateo's sessions are 87 minutes long
Ron's sessions are 90 minutes long
Explanation:
Here, we want to get the duration for the episodes
Let the duration of Mateo's episodes be m and that of Ron be r
Let us start with the information about last year:
[tex]\begin{gathered} 19(m)\text{ + 45\lparen r\rparen = 5703 } \\ 19m\text{ + 45r = 5703} \end{gathered}[/tex]This year, we have it that:
[tex]\begin{gathered} 12(m)\text{ + 45\lparen r\rparen = 5094} \\ 12m\text{ + 45r = 5094} \end{gathered}[/tex]The two equations to solve simultaneously are:
[tex]\begin{gathered} 19m\text{ + 45r = 5703} \\ 12m\text{ + 45r = 5094} \end{gathered}[/tex]Subtract equation ii from i
[tex]\begin{gathered} 7m\text{ = 609} \\ m\text{ = }\frac{609}{7} \\ m\text{ = 87} \end{gathered}[/tex]To get the value of r, we substitute the value m into any of the equations as follows:
[tex]\begin{gathered} 12(87)\text{ + 45r = 5094} \\ 45r\text{ = 5094 - 1044} \\ 45r\text{ = 4050} \\ r\text{ = }\frac{4050}{45} \\ r\text{ = 90} \end{gathered}[/tex]