The $12+8 = $20 that Nancy had before brunch on Sunday was 2/3 of the money she had before her mall trip on Saturday. Then she had $30 before going to the mall. That amount was 3/4 of her weekly allowance. Her allowance was ...
... E) $40
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It often works well to work problems like this backward, starting with what you know at the end of the series of transactions.
Let Nancy's allowance be represented by "a". Then
... movie cost = 1/4·a
remaining amount = a - (1/4·a) = 3/4·a
... mall expense = (1/3)·(3/4·a) = (1/4)·a
remaining amount after mall = (3/4)·a - (1/4)·a = (2/4)·a = (1/2)·a
... Sunday brunch = $12
remaining amount after brunch = (1/2)·a - $12 = $8
... 1/2·a = $20 . . . . . . add $12
... a = 2·$20 = $40 . . . . . multiply by 2
