Final answer:
By setting Chang's number of text messages as the variable 'C', we use the provided relationships to find that Chang sent 18 messages, Manuel sent 72, and Donna sent 26, totaling 116 messages.
Step-by-step explanation:
Let's denote Chang's number of messages as C, Manuel's as M, and Donna's as D. According to the problem, Manuel sent 4 times as many messages as Chang (M = 4C) and Donna sent 8 more messages than Chang (D = C + 8). The total number of messages sent by all three is 116 (C + M + D = 116).
Substituting the expressions for M and D in terms of C into the total, we get:
C + 4C + (C + 8) = 116
Combine like terms:
6C + 8 = 116
Subtract 8 from both sides:
6C = 108
Divide by 6:
C = 18
Now that we have Chang's number of messages, we can find out Manuel's and Donna's:
M = 4 × 18 = 72 (Manuel's messages),
D = 18 + 8 = 26 (Donna's messages)
To confirm, let's check that the sum equals 116:
18 (Chang) + 72 (Manuel) + 26 (Donna) = 116
The correct answer is therefore: Chang sent 18 messages, Manuel sent 72, and Donna sent 26, totaling 116 messages.