Which Alice?

ALICE IN PUZZLE-LAND
also wants some tarts. Well, the Hatter had already set the places,
and had given himself three times as many tarts as he had given the
March Hare, and the Dormouse had been given only half as many
as the March Hare,"
"The poor Dormouse really had the worst of the bargain!" said
Alice sympathetically.
"Decidedly!" replied the Gryphon. "Anyway, the Hatter had
twenty more tarts than the Dormouse."
"That's an enormous number of tarts!" said Alice.
"Not really," replied the Gryphon, "because the tarts were
extremely small. Anyway, how many tarts did each one have?
"And you don't need no algebra!" he added.
What is the solution?
THE TABLES ARE TURNED! "The Hatter always seems to get
the best of the bargain!" remarked Alice.
"Usually, yes," replied the Gryphon, "but on one occasion, the
other two got even! On this occasion, the Hatter had set the places,
and put all the tarts on his own plate—he left nothing for the March
Hare or the Dormouse. Now the table was set out on the lawn, and
when the Hatter went into the house to brew the tea, the March
Hare quickly took five-sixteenths of the tarts from the plate and ate
them. Then the Dormouse ate up seven-elevenths of the remaining
tarts. This left eight tarts for the Hatter. How many tarts did each
of the other two eat?"
HOW MANY FAVORITES? "Here's a slightly different kind of
puzzle," said the Gryphon. "One day the Queen of Hearts was
entertaining thirty guests. She had one hundred tarts to divide
among them. Rather than cut any tart in pieces, she decided to give
four tarts apiece to each of her favorites, and three apiece to each of
the other guests. How many favorites did she have?"
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