Final answer:
By setting up equations based on the given relationships, we determined that Maya sent 18 messages, Alan sent 11 messages, and Felipe sent 72 messages during the weekend.
Step-by-step explanation:
The student is asking a math problem involving writing and solving equations based on the given conditions to find out how many messages were sent by Maya, Alan, and Felipe. Let's call the number of messages Maya sent 'm'. According to the problem, Felipe sent 4 times as many messages as Maya, which can be written as '4m'. Alan sent 7 fewer messages than Maya, so he sent 'm - 7' messages. Together, they sent a total of 101 messages, which gives us the equation:
m + 4m + (m - 7) = 101
Combining like terms, we get:
6m - 7 = 101
Adding 7 to both sides:
6m = 108
Dividing by 6:
m = 18
So, Maya sent 18 messages. Now we can find out how many messages Felipe and Alan sent:
Felipe: 4m = 4 × 18 = 72 messages
Alan: m - 7 = 18 - 7 = 11 messages
In conclusion, Maya sent 18 messages, Alan sent 11 messages, and Felipe sent 72 messages.