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:
[tex] \left \{ {{x+y=43} \atop {z+y=30}} \right. [/tex]
We will subtract the bottom equation from the top:
[tex] \left \{ {{x+y=43} \atop {-(z+y=30)}} \right.
\\
\\x-z=13 [/tex]
We will now take this and the last equation as a system; this time, we will eliminate z by adding the two equations:
[tex] \left \{ {{x-z=13} \atop {+(x+z=55)}} \right.
\\
\\2x=68 [/tex]
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
