Grandpa's Rock Cakes
Grandpa made a super-heavy rock cake. Five people have guessed the weight of the cake. Can you work out the weight of his cake?
Age
11 to 14
Challenge level
Problem
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.
Student Solutions
The cake weighed 5 130g.
The range of the guesses (5 040g, 5 060g, 5 110g, 5 120g and 5 150g) is 110 so the two 'wild' estimates must both be low or both high.
Since the difference between 5 040 and 5 060 is 20, 5 040 is 90 out and 5 060 is 70 out.
The range of the guesses (5 040g, 5 060g, 5 110g, 5 120g and 5 150g) is 110 so the two 'wild' estimates must both be low or both high.
Since the difference between 5 040 and 5 060 is 20, 5 040 is 90 out and 5 060 is 70 out.