Answered

Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A 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)
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.