Let's assume the following:
L - indicates the number of text messages sent by Lisa
J - by Juan, and
K - by Kareem
Having said that, we propose the following equations
[tex]\begin{gathered} L+J+K=100 \\ K=3\cdot J \\ L=J-5 \end{gathered}[/tex]Now, let's solve this system of equations
1. from L=J-5, then
[tex]\begin{gathered} J-5+J+K=100 \\ 2J+K-5=100 \\ \end{gathered}[/tex]2. from K=3J, then
[tex]\begin{gathered} 2J+3J-5=100 \\ 5J-5=100 \\ 5J=100+5 \\ J=\frac{105}{5} \\ J=21 \end{gathered}[/tex]- we can see that Juan sent 21 text messages
3. substitute J=21 in L=J-5
[tex]\begin{gathered} L=21-5 \\ L=16 \end{gathered}[/tex]- thus, Lisa sent 16 text messages
4. substitute J=21 in K=3J
[tex]\begin{gathered} K=3\cdot21 \\ K=63 \end{gathered}[/tex]- therefore, Kareem sent 63 text messages
In conclusion, they sent the following number of messages
Lisa: 16
Juan: 21
Kareem: 63
