Final answer:
The three numbers the student is thinking of are 83, 72, and 64. This was determined by setting up a system of equations based on the given sums of the number pairs, solving for the total sum of all three numbers, and then individually subtracting the pair sums from the total sum to find each number.
Step-by-step explanation:
The question revolves around finding three specific numbers given the sums of them when paired. To solve this problem, we will use a system of equations which is a common method in algebra. Let's denote the three unknown numbers as A, B, and C.
According to the question, we have the following sums when these numbers are added in pairs:
- A + B = 155
- A + C = 147
- B + C = 136
To find the individual values of A, B, and C, we add all three equations together to get 2A + 2B + 2C which equals the sum of all pair sums:
2A + 2B + 2C = 155 + 147 + 136
Divide by 2 to get A + B + C:
A + B + C = 219
Now we can solve for any of the single variables by subtracting one of the pair sums from 219. For example, to find A, we subtract the sum of B + C from 219:
A = 219 - (B + C)
A = 219 - 136
A = 83
Using the same method, we can find B and C:
B = 219 - (A + C)
B = 219 - 147
B = 72
Finally, C:
C = 219 - (A + B)
C = 219 - 155
C = 64
So the three numbers are 83, 72, and 64.