### Kate's Date

Weekly Problem 31 - 2012
When Kate ate a giant date, the average weight of the dates decreased. What was the weight of the date that Kate ate?

### Balancing the Books

Weekly Problem 32 - 2012
How many visitors does a tourist attraction need next week in order to break even?

### 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:

38.

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.
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