Respuesta :
Let's say that L represents the text messages sent by Lisa, J by Juan and K by Kareem.
in this way, we have the following equations
[tex]\begin{gathered} L+J+K=100 \\ K=3\cdot J \\ L=J-5 \end{gathered}[/tex]Now, let's solve the equations system
1. substitute l = j-5 and simplify
[tex]\begin{gathered} J-5+J+K=100 \\ 2J+K-5=100 \end{gathered}[/tex]2. substitute k=3j and simplify
[tex]\begin{gathered} 2J+3J-5=100 \\ 5J=100+5 \\ J=\frac{105}{5} \\ J=21 \end{gathered}[/tex]- We have found that Juan has sent 21 text messages
3. for K=3J substitute J=21
[tex]\begin{gathered} K=3J \\ K=3\cdot21 \\ K=63 \end{gathered}[/tex]- we found that Kareem has sent 63 text messages
4. for L=J-5 substitute J=21
[tex]\begin{gathered} L=J-5 \\ L=21-5 \\ L=16 \end{gathered}[/tex]- Thus, Lisa sent 16 text messages
In conclusion, the solution to the system of equations is the following:
J = 21, K = 63, L = 16
