Answered

At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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.

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.