Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

three bags of potatoes and four cases of corn cost $40. Five bags of potatoes and two cases of corn cost $34. Find the cost of one bag of potatoes and the cost of one case of corn.

Sagot :

RedRicin
Use variables and set up equations.

[tex]3p + 4c = 40 \\ 5p + 2c = 34[/tex]

Next, get one variable with equal coefficients.

[tex]3p + 4c = 40 \\ 10p + 4c = 68\ (multiplied\ both\ sides\ by\ 2)[/tex]

Then get it alone on one side.

[tex]4c = 40-3p \\ 4c = 48-10p[/tex]

Now we can use substitution. Since [tex]40-3p = 4c[/tex], substitute [tex]40-3p[/tex] for [tex]4c[/tex] in the other equation and you'll get an equation with just one variable to simplify and solve.

[tex]40-3p = 68-10p \\ 40+7p = 68 \\ 7p = 28 \\ \boxed{p = 4}[/tex]

We can then use [tex]p = 4[/tex] in an earlier equation to find [tex]c[/tex].

[tex]5p + 2c = 34 \\ 5*4 + 2c = 34 \\ 20 + 2c = 34 \\ 2c = 14 \\ \boxed{c=7}[/tex]

Panoyin
3p + 4c = 40 ⇒ 15p + 20c = 200
5p + 2c = 34 ⇒ 15p +   6c = 102
                                    14c = 98
                                     14     14
                                        c = 7
                            5p + 2(7) = 34
                              5p + 14 = 34
                                    - 14  - 14
                                      5p = 20
                                       5      5
                                        p = 4
                                  (p, c) = (4, 7)
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.