Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

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?

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 Pa class=

Sagot :

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.

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.