Explanation
Let the number of messages John sent be x. Therefore since Lena sent 5 fewer messages than John, therefore, the number of messages sent by Lena becomes
[tex]x-5[/tex]
Also, Brian sent three times as many messages as john. This implies Brena messages as
[tex]3x[/tex]
Recall that all together, the trio sends a total of 110 messages. We can then combine the previous statements below.
[tex]\begin{gathered} \text{Lena + John +Brian =110} \\ x+x-5+3x=110 \\ 5x=110+5 \\ 5x=115 \\ x=\frac{115}{5} \\ x=23 \end{gathered}[/tex]
Therefore,
[tex]\begin{gathered} \text{John messages = 23} \\ \text{Lena messages =x-5= }23-5\text{ =18} \\ \text{Brian messages =}3x=3\times23=69 \end{gathered}[/tex]
Answer:
Lena sent 18 messages
John sent 23 messages
Brian sent 69 messages
