This past Saturday, Jessy and Alan told a total of 11+7 = <<11+7=18>>18 jokes together.
Since Jessy told eleven jokes this past Saturday, when he doubles the number of jokes next Saturday, the number of jokes will be 2*11= 22 next Saturday.
At the same time, after telling seven jokes this Saturday, when he doubles the number of jokes next Saturday, Alan will tell 2*7 = <<2*7=14>>14 jokes.
Next Saturday, they will tell 14+22 = <<14+22=36>>36 jokes together.
In total, the number of jokes will be 36+18 = <<36+18=54>>54 jokes on the two Saturdays.
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