Final answer:
The number of messages each person sent is determined using algebraic expressions. After setting up the equations based on the details provided, we calculate that Ann sent 23 messages, Justin sent 31 messages, and Brian sent 69 messages, totaling 123 messages. This correct distribution of messages doesn't match the provided options.
Step-by-step explanation:
We can solve this problem by setting up algebraic expressions for each person's number of sent messages and creating equations based on the information provided. iet's let A represent the number of messages Ann sent. According to the problem, Justin sent 8 more messages than Ann, so we can express this as J = A + 8. Brian sent three times as many messages as Ann, which gives us B = 3×A. Since we know the total number of messages sent by all three of them was 123, we can write the following equation to represent this total:
A + (A + 8) + 3×A = 123
Simplifying the equation:
5×A + 8 = 123
Now, if we solve for A:
5×A = 115
A = 23
Ann sent 23 messages. For Justin's total, we add 8:
J = 23 + 8 = 31
Justin sent 31 messages. For Brian's total, we multiply Ann's total by 3:
B = 3×23 = 69
Brian sent 69 messages.
When we add these up (23 + 31 + 69), they do total 123 messages, which confirms our calculations are correct. However, since these numbers aren't among the given answer choices, there must be a mistake in the provided options or in the question's structure. therefore, the correct allocation of messages is Ann: 23, Justin: 31, and Brian: 69, which does not match any of the answer choices (a, b, c, or d).