Mathematics
Grey Kangaroo
2023
22

22

Some mice live in three neighbouring houses. Last night, every mouse left its house and moved to one of the other two houses, always taking the shortest route. The numbers in the diagram show the number of mice per house, yesterday and today. How many mice used the path at the bottom of the diagram ?

A 9 B 11 C 12 D 16 E 19

Answer

B

SOLUTIOn

Let the number of mice that travelled from the left-hand house to the right-hand house along the bottom path be x and the number of mice that travelled from the right-hand house to the left-hand house be y. Therefore, since every mouse changed house last night, 8 − x mice travelled from the left-hand house to the top house and 7 − y mice travelled from the right-hand house to the top house. Hence, since there were then 4 mice in the top house, we have 8 − x + 7 − y = 4 and so x + y = 11. Therefore the number of mice that travelled along the bottom path in the diagram is 11.

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