Question

Easy looking math problem but hard

Answer 1

3.5 4.5

9.5 3.5

Explanation:

The top left box is x

The top right box is y

The bottom left box is z

The bottom right box is n

Across

x+y =8

z-n =6

Down

x+z =13

y+n = 8

Adding

z-n =6

y+n = 8

----------------

z+y = 14

Subtracting

x+y =8

-(x+z =13)

-------------------

y -z = -5

Adding these two new equations together

z+y = 14

y -z = -5

--------------------

2y = 9

or y = 4.5

Now we can solve for x

x+y = 8

x+4.5 =8

x = 3.5

And solving for z

x+z = 13

3.5 +z =13

z = 9.5

Finally for n

y+n = 8

4.5 +n = 8

4.5 +n = 8

n = 3.5

Answer 2

3.5 + 4.5 = 8

+ +

9.5 - 3.5 = 6

= =

13 8

Explanation:

Let us make equations and solve them to find the missing numbers

Assume that the empty square in the 1st row and 1st column is x, the empty square in the 1st row and 2nd column is y

∵ The sum of the two empty squares in the 1st row is 8

∴ x + y = 8 ⇒ (1)

∵ The sum of the empty squares in the 2nd column is also 8

and one of them is y

∴ The empty square in the 2nd row and 2nd column is also x

Assume that the empty square in the 2nd row and 1st column is z

∵ The sum of the empty squares in the 1st column is 13

∴ x + z = 13 ⇒ (2)

∵ The difference between the empty squares in the 2nd row is 6

∴ z - x = 6 ⇒ (3)

Add equations (2) and (3) to eliminate x

∵ (x - x) + (z + z) = (13 + 6)

∴ 2z = 19

- Divide both sides by 2

∴ z = 9.5

Substitute the value of z in equation (2) or (3) to find x

∵ x + 9.5 = 13

- Substitute 9.5 from both sides

∴ x = 3.5

Substitute the value of x in equation (1) to find y

∵ 3.5 + y = 8

- Subtract 3.5 from both sides

∴ y = 4.5

3.5 + 4.5 = 8

+ +

9.5 - 3.5 = 6

= =

13 8