# Can you spot the trick?

Algebra Level 5

$\large \begin{cases} {a+b=8} \\ {ab+c+d=23} \\ {ad+bc=28} \\ {cd =12} \end{cases}$

Let $$a,b,c$$ and $$d$$ be four real numbers satisfying the system of equations above.

What is the sum of all possible different values of $$a+2b+3c+4d$$?

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