In a number square, the sum of the numbers in each row, column, and main diagonal is the same.

Find the sum of the number square.

a 7 2
1 5 b
8 c 4

Add the diagonal to find the sum. That should lead you to the answers.

I hope this helps. Thanks for asking.

To find the sum of the number square, we need to determine the values of the missing numbers represented by the variables a, b, and c.

Since the sum of the numbers in each row, column, and main diagonal is the same, we can use this information to set up a system of equations to solve for a, b, and c.

Let's label the sum of each row, column, and diagonal as S.
For the rows, we have the equations:

a + 7 + 2 = S equation (1)
1 + 5 + b = S equation (2)
8 + c + 4 = S equation (3)

For the columns, we have:

a + 1 + 8 = S equation (4)
7 + 5 + c = S equation (5)
2 + b + 4 = S equation (6)

For the main diagonal, we have:

a + 5 + 4 = S equation (7)

Simplifying these equations, we get:

a + 9 = S equation (8)
b + 6 = S equation (9)
c + 12 = S equation (10)
a + 9 = S equation (11)
c + 12 = S equation (12)
b + 6 = S equation (13)
a + 9 = S equation (14)

From equations (8), (9), and (10), we can say that:

a = S - 9 equation (15)
b = S - 6 equation (16)
c = S - 12 equation (17)

Now, let's substitute equations (15), (16), and (17) back into equations (7), (13), and (14) respectively:

S - 9 + 5 + 4 = S equation (18)
(S - 6) + 6 = S equation (19)
S - 9 + 9 = S equation (20)

Simplifying equations (18), (19), and (20), we get:

S = 18 equation (21)

Now we have found the value of S, which is 18. Therefore, the sum of the number square is 18.