Primary School Maths - Too Clever By 0.5

I was looking at the BBC news web pages and came across this item - "Why parents can't do maths today". It reminded me of a parenting moment.

When eldest son was still in primary school - penultimate year it was - he was given the following maths problem:

You are given two bags. One bag contains coins each with a face value of £7; the other bag contains coins each with a face value of £9. The sum total amount of both bags is £2500. How many coins in each bag?

So my son asks me for help with this one. Now I am not a mathematician but I studied maths to gain entry to University and I used a lot of it in my PhD. I can program too after a fashion. Realising that we have only one equation and two unknowns but knowing that the answers had to be natural numbers I wrote a quick script to iterate through all possible answers that resulted in natural number values for the number of £7 and £9 coins totalling 2500. (It was a while ago so don't ask for the code - all I remember was there 42 answers - Douglas Adams would have been proud!).

So I wrote to the teacher expressing a concern that this level of question was a bit steep for primary school...

In the mean time I posed the question at a gathering of people who think they knows maths - PhD in Maths, Physics, Geophysics, Engineering etc. They were all a bit perplexed!

So the teacher's letter came back and explained that the Heinmann maths text the children followed suggested the following method:

£2500 - well that is a bit like £25 if you ignore the zeros, so

( 2 x £9 ) + ( 1 x £7 ) = £25

therefore

( 200 x £9 ) + ( 100 x £7 ) = £2500

So it turns out my son had been told this method about disregarding the zeroes. Had my son told me it would have helped...

But would the teacher mark the other 41 possible answers wrong? I think they would.