Question

Write a system of equations to describe the situation below, solve using elimination, and fill inthe blanks.Mateo hosts a podcast about computers, and Ron hosts a podcast about parenting. Bothpodcasts have a set duration for each episode. Last year, Mateo released 19 episodes and Ronreleased 45 episodes, for a total of 5,703 minutes of content. This year, Mateo released 12episodes and Ron released 45 episodes, which lasted a total of 5,094 minutes. How long iseach episode?

Answer 1

Mateo's sessions are 87 minutes long

Ron's sessions are 90 minutes long

Step-by-step 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:

`\begin{gathered} 19(m)\text{ + 45\lparen r\rparen = 5703 } \\ 19m\text{ + 45r = 5703} \end{gathered}`

This year, we have it that:

`\begin{gathered} 12(m)\text{ + 45\lparen r\rparen = 5094} \\ 12m\text{ + 45r = 5094} \end{gathered}`

The two equations to solve simultaneously are:

`\begin{gathered} 19m\text{ + 45r = 5703} \\ 12m\text{ + 45r = 5094} \end{gathered}`

Subtract equation ii from i

`\begin{gathered} 7m\text{ = 609} \\ m\text{ = }(609)/(7) \\ m\text{ = 87} \end{gathered}`

To get the value of r, we substitute the value m into any of the equations as follows:

`\begin{gathered} 12(87)\text{ + 45r = 5094} \\ 45r\text{ = 5094 - 1044} \\ 45r\text{ = 4050} \\ r\text{ = }(4050)/(45) \\ r\text{ = 90} \end{gathered}`