Final answer:
The number that goes in the middle circle to have each diagonal sum up to 9 is 3. We can determine this by process of elimination and trying out different combinations of numbers that sum up to 9.
Step-by-step explanation:
To solve this problem, we need to place numbers 1 through 5 in circles so that each diagonal sums up to 9. Let's start by labeling the center circle with a variable, for example, 'x'. Since the diagonals must all add up to 9 and we know all the other numbers are 1, 2, 3, 4, and 5, we can deduce which number 'x' should be.
Let's consider the combinations of numbers we can use. The numbers alongside the center circle on the diagonal could be (1,3), (2,2), or (4,1). However, since there are only unique numbers from 1 to 5, the combination cannot have the same numbers. Therefore, the pairs we can use would be (1,3) or (4,1). After trying out those combinations, we can see that when x is 3, the numbers on the diagonal adding to 3 would be 1 and 5 or 4 and 2, both of which give us a sum of 9.
Therefore, the correct answer is c) 3, which is the number that goes in the middle circle to ensure the sum of each diagonal is 9.