I'm new here, and I'm hoping someone can help out. My 10 year old son has been set a maths problem, which I can't solve. I've got a PhD in neuroscience and do a fair amount of matlab stuff (data analysis, image processing) on a daily basis, but I can't work this out.

The problem is expressed in words, but I've read it through a dozen times and I'm sure it boils down to the following:

a + b = 55

b + c = 43

c + d = 42

d + e = 37

They are asked to find the value of e. But this is 4 equations with 5 unknowns. Is there really a unique solution for this system of equations? Where am I going wrong?

If you set one of the variable to 0 you can solve for the rest, of course, but I'm pretty sure this is not what they are meant to do. The hint says it's easiest to start by working out the value of c.

I'm lost, any help would be most appreciated!

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The exact question is:

> 
> The following people take part in a school trip: 55 boys and girls; 43 girls and fathers; 42 fathers and mothers and 37 mothers and teachers. How many teachers took part in the school trips?
> 
> 
> 

Assuming the classes are mutually exclusive (i.e. no teachers are also parents), I'm pretty sure that is the set of equations I posted. The other problems in the same homework are similar in form but all have 1 additional piece of information: the total number (e.g., a + b + c + d + e = 100). Those ones are solvable no problem.