Answer:
Joe sent 23 messages
Trey sent 69 messages
Rachel sent 30 messages
Explanations:
Let the number of messages sent by Rachel be r
Let the number of messages sent by Trey be t
Let the number of messages sent by Joe be j
The total number of messages sent by the three of them is 122
r + t + j = 122...........(1)
Trey sent 3 times as many messages as Joe
t = 3j................(2)
Racheal sent 7 more messages than Joe
r = 7 + j........(3)
Substitute equations (2) and (3) into equation (1)
(7 + j) + 3j + j = 122
7 + 5j = 122
5j = 122 - 7
5j = 115
j = 115 / 5
j = 23
Joe sent 23 messages
Substitute the value of j into equation (2)
t = 3j
t = 3(23)
t = 69
Trey sent 69 messages
Substitute the value of j into equation (3)
r = 7 + 23
r = 30
Rachel sent 30 messages