Grandpa has made one of his special giant rock cakes.
At his 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?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.