Equations and polynomials?

Algebra Level 5

Let a,b,c,d,ea, b, c, d, e be real numbers that satisfy the equations:

c+a=15c+a=15

ac+b+d=85,ac+b+d=85,

ad+bc+e=225,ad+bc+e=225,

ae+bd=274,ae+bd=274,

be=120.be=120.

Find the sum of all possible values of ee.

Here's a hint (a simpler problem)

This problem is part of the set ... and polynomials

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