Final answer:
To solve this problem, we can use algebraic equations to represent the relationships between Lisa, Hong, and Alonzo's messages. Hong sent 23 messages, Lisa sent 17 messages, and Alonzo sent 69 messages.
Step-by-step explanation:
To solve this problem, we can use algebraic equations to represent the relationships between Lisa, Hong, and Alonzo's messages.
Let's start by defining the number of messages Hong sent as 'x.' Lisa then sent 6 fewer messages, so the number of messages she sent is 'x - 6.' Alonzo sent 3 times as many messages as Hong, so the number of messages he sent is '3x.'
Since the total number of messages sent is 109, we can set up an equation: x + (x - 6) + 3x = 109
Simplifying this equation, we get 5x - 6 = 109.
By adding 6 to both sides and dividing by 5, we find that x = 23.
Therefore, Hong sent 23 messages, Lisa sent 17 messages (23 - 6), and Alonzo sent 69 messages (3 * 23).