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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.

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RedRicinidn
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]

Panoyinidn
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)
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