Let the trapezoid be [tex] x [/tex], the moon [tex] y [/tex].We also know that the diamond is worth 2, so 2 diamonds are worth 4.
The system is in equilibrium, so we have
[tex] x=y+2\text{diamonds} \iff x = y+4 [/tex]
Also, all the pieces together sum up to 30:
[tex] x+y+4 = 30 \iff x+y = 26 [/tex]
Substitute [tex] x = y+4 [/tex] in the second equation:
[tex] x+y = 26 \iff y+4+y = 26 \iff 2y+4 = 26 \iff 2y = 22 \iff y = 11[/tex]
Which implies
[tex] x = 11+4 = 15 [/tex]
