Let b1 represent the length of the first base, and b2 the length of the second one. Then we have ...
... b1 = -19 + 5b2 . . . . . . . . . . . . the relation between the base lengths
... Area = 1/2(b1 +b2)h . . . . . . . formula for area of a trapezoid
... 477 = (1/2)(b1 + b2)·18 . . . . . filling in the given values
Dividing the second equation by 9, we get
... b1 + b2 = 53
Subtracting b2, we get an expression for b1 that can be set equal to that given by the first equation.
... b1 = 53 - b2 = 5b2 -19
... 72 - b2 = 5b2 . . . . . . . . . add 19
... 72 = 6b2 . . . . . . . . . . . . . add b2
... 12 = b2 . . . . . . . . . . . . . . divide by 6
... b1 = 53 - 12 = 41 . . . . . . . from our second expression for b1
The longer base has length 41 feeet.