Final answer:
Christine sent 20 messages, Greg sent 28 messages, and Henry sent 80 messages.
Step-by-step explanation:
To solve this problem, let's assign variables to represent the number of messages sent by each person. Let C represent the number of messages Christine sent, G represent the number of messages Greg sent, and H represent the number of messages Henry sent. We are given the following information:
- The total number of messages sent is 128: C + G + H = 128
- Henry sent 4 times as many messages as Christine: H = 4C
- Greg sent 8 more messages than Christine: G = C + 8
We can now substitute the values from the second and third equations into the first equation to solve for the variables. Substituting 4C for H and C + 8 for G, we get C + (C + 8) + 4C = 128, which simplifies to 6C + 8 = 128. Subtracting 8 from both sides, we have 6C = 120. Dividing both sides by 6, we find that C = 20.
Now that we know the value of C, we can substitute it back into the second and third equations to find the values of G and H. Substituting 20 for C in the equation H = 4C, we get H = 4(20), which equals 80. Substituting 20 for C in the equation G = C + 8, we get G = 20 + 8, which equals 28.
Therefore, Christine sent 20 messages, Greg sent 28 messages, and Henry sent 80 messages. So, the correct answer is option B: Christine: 20, Greg: 28, Henry: 80.