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'Grandpa's Rock Cakes' printed from http://nrich.maths.org/
Grandpa has made another of his special super-heavy giant rock cakes. At his birthday party, five of the guests tried to guess the weight of the cake.
Their guesses were 5 040g, 5 060g, 5 110g, 5 120g and 5 150g.
Actually, none of them was right. Only two were more than 30 grams out, and those guesses were out by 70g and 90g.
What was the weight of the cake?
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This problem is taken from the UKMT Mathematical Challenges.