Question

A clothing store is donating socks to various charities. The store gave 6 regular packs and 5 value packs to a homeless shelter, which contained a total of 163 pairs of socks. For foster children, the store donated 6 regular packs and 4 value packs, which equaled 146 pairs. How many pairs of socks are in each pack?

Answer 1

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

`6r+5v=163`

Similarly, since the store donated 6 regular packs and 4 value pack which add 146 pair of socks, we can write

`6r+4v=146`

Then, we have the following system of equations:

`\begin{gathered} 6r+5v=163\ldots(a) \\ 6r+4v=146\ldots(b) \end{gathered}`

Solving by elimilation method.

By multiplying equation (b) by -1, we have an equivalent system of equations:

`\begin{gathered} 6r+5v=163 \\ -6r-4v=-146 \end{gathered}`

Then, by adding both equations, we have

`v=17`

Now, in order to obtain the number of socks in a regular pack, we must substitute the last result into equation (a). It yields,

`6r+5(17)=163`

which gives

`6r+85=163`

By subtracting 85 to both sides, we have

`6r=78`

Then, r is given by

`\begin{gathered} r=(78)/(6) \\ r=13 \end{gathered}`

Therefore, the answer is: There are 13 pairs of socks in each regular pack and 17 pairs in each value pack.