11 Plus Exams Forum

Maths question

In a street, the refuse bins are emptied every 9 days. The recycling boxes are emptied every 5 days. Both the bins and boxes are emptied together on the 1 st March.
How many times will both the bins and the boxes be emptied on the same day from the 1 st March to the 31 st May?

Thanks

Anna

Let's call the 1st March Day 0.

On Day 5, 10, 15 etc. the refuse bins will be emptied.

On Day 9, 18, 27 etc. the recycling bins will be emptied.

The days when both are emptied are the days which are a multiple of both 5 and 9. The common multiples of 5 and 9 are 45, 90, 135 etc.

Within the range from March 1st to May 31st, there are 92 days (31 from March, 30 from April and 31 from May). If March 1st = Day 0, then 31st May = Day 91. Both bins are emptied on Day 45 and Day 90, so there are 2 times both will be emptied together from 1st March to 31st May.

3 times surely?

I'd do this as - March + April + May = 31+30+31 = 92 days
First common multiple of 5 and 9 is 45 - so every 45 days

Collection on Day 1 (March 1st)
then every 45 days - so subsequent collections on days 46 and 91 means 3 collections altogether.

You are right, I ignored the very first collection for some reason!