Question

Enter numbers in the circles so that the numbers on each line equal the sum of the numbers at each end.

Answer 1

The correct answers are:

Top circle: 34

Bottom left: 9

Bottom right: 21

Explanation:

Let the top circle be x, let the bottom left circle be y, and the bottom right circle be z.

Following the diagram, we have the following equaitons:

x+y = 43

y+z = 30

x+z = 55

Taking the first two equations as a system, we will eliminate y:

$\left \{ {{x+y=43} \atop {z+y=30}} \right.$

We will subtract the bottom equation from the top:

$\left \{ {{x+y=43} \atop {-(z+y=30)}} \right. \\ \\x-z=13$

We will now take this and the last equation as a system; this time, we will eliminate z by adding the two equations:

$\left \{ {{x-z=13} \atop {+(x+z=55)}} \right. \\ \\2x=68$

Divide each side by 2:

2x/2 = 68/2

x = 34

Substitute this into the first equation:

x+y = 43

34+y = 43

Subtract 34 from each side:

34+y-34 = 43-34

y = 9

Substitute this into the second equation:

y+z = 30

9+z = 30

Subtract 9 from each side:

9+z-9 = 30-9

z = 21

Answer 2

Simple 
in the top circle write 34
in the left bottom write 9
in right bottom write 21
so now 9 + 21 =30
34 + 9 = 43
34 + 21 =55
so it fits in circle

SMILE