Question 1048965
.
Hi
in a textbook the following problem was as follows. James has some matchsticks and sachets. 
If one matchstick is put into each sachet there are 2 matchsticks left.
If he puts 2 matchsticks into each sachet he will have 24 sachets left. 
The solutions are m-s = 2 and s-m/2 = 24.

Can u help me understand how these equations were derived.

thank you
~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
There is no need to explain the first equation.
It is the direct and literal math translation  of the condition
    ("If one matchstick is put into each sachet there are 2 matchsticks left.")


Regarding the second equation, firstly, the condition clearly assumes and means that the number of matchsticks is even.

Secondly, the number of sachets containing exactly 2 matchsticks is {{{m/2}}}. The remaining s - {{{m/2}}} sachets are without matchsticks, and their number is 24, 
    in accordance with the condition.

It is exactly what the second equation says.
</pre>