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Grandpa's Rock Cakes

Weekly Problem 34 - 2012
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?

Average Surroundings

Stage: 3 Short Challenge Level: Challenge Level:1


We are given that: $$A=\frac {B+31+64+20}{4}=\frac {B+115}{4}$$ and
$$B=\frac {A+18+54+38}{4}=\frac{A+110}{4}$$
$$4A=B+115$$ Subbing in the second equation gives
$$4A=\frac {A+110}{4}+115$$ so $$16A=A+110+460=A+570$$.
Therefore $$A=\frac {570}{15}=38$$.

This problem is taken from the UKMT Mathematical Challenges.