TYPE OF CROSSING COST (£)
Zebra Crossing 1800
Pelican Crossing 16800
Puffin Crossing 22000
The council spends £184,200 on 10 crossings. How many of each type do they buy?
There is a way of doing it relatively quickly.
If you observed that two of the choices have 8 in the hundreds place while the other has 0, and the total has 2 in the hundreds place, then can work out there must either be 4 or 9 distributed between Zebra and Pelican. It is obviously not 9 because it wouldn't come to such a large total if you only had 1 of the Puffins.
That is 4 between Zebra and Pelican, thus 6 of the Puffin.
184,200 - (6 x Puffins) = 52,200
Then it is a short step to realising that this must be mostly Pelicans as you wouldn't reach this number with Zebras so it is 3 Pelicans and 1 Zebra, ie. £16,800 x 3 + £1800
This took me 2 minutes, although obviously if I hadn't spotted the hundreds thing, it would have been a lot longer.
I always work on the premise that an 11 year old child would have only 5 minutes, tops, to do these and therefore there must be a relatively simply way to do it that does not involve algebra, simultaneous equations etc.. It is more a case of having a 'feel' for numbers and how they work.