Let r and v be the number of socks ina regular pack and value pack, respectively. Since the store gave 6 regular packs and 5 value packs which contained 163 pair of socks, we can write
[tex]6r+5v=163[/tex]Similarly, since the store donated 6 regular packs and 4 value pack which add 146 pair of socks, we can write
[tex]6r+4v=146[/tex]Then, we have the following system of equations:
[tex]\begin{gathered} 6r+5v=163\ldots(a) \\ 6r+4v=146\ldots(b) \end{gathered}[/tex]Solving by elimilation method.
By multiplying equation (b) by -1, we have an equivalent system of equations:
[tex]\begin{gathered} 6r+5v=163 \\ -6r-4v=-146 \end{gathered}[/tex]Then, by adding both equations, we have
[tex]v=17[/tex]Now, in order to obtain the number of socks in a regular pack, we must substitute the last result into equation (a). It yields,
[tex]6r+5(17)=163[/tex]which gives
[tex]6r+85=163[/tex]By subtracting 85 to both sides, we have
[tex]6r=78[/tex]Then, r is given by
[tex]\begin{gathered} r=\frac{78}{6} \\ r=13 \end{gathered}[/tex]Therefore, the answer is: There are 13 pairs of socks in each regular pack and 17 pairs in each value pack.
