Question

How do you start this and find the weight of each shape? I do not remember doing this in class.

Answer 1

Let's say   make the shapes, some variable name

say   

⛁    ⚪     ◽    ▯
a     b      c     d

so.. if take those are the shapes provided

then we can take a look at the first set and we can say that

2a + b + c = 20

a + 4d + b = 19

a + c = 9

3c + d + a = 19 

thus     $\bf \begin{cases} 2a + b + c = 20\\ a + 4d + b = 19\\ a + c = 9\\ 3c + d + a = 19 \end{cases}\\\\ -----------------------------\\\\ a+c=9\implies \boxed{c}=9-a\qquad thus \\\\\\ 2a+b+\boxed{9-a}=20\implies \underline{b}=11-a\impliedby thus \\\\\\ a+4d+\underline{11-a}=19\implies d=\cfrac{8}{4}\implies d=2\\\\ -----------------------------\\\\ then\qquad 3\left(\boxed{9-a } \right)+\boxed{2}+a=19\implies 27-3a+2+a=19 \\\\\\ 10=2a\implies 5=a$

and surely you can find the other two