Question

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.

Answer 1

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)

Answer 2

Use variables and set up equations.


`3p + 4c = 40 \\ 5p + 2c = 34`

Next, get one variable with equal coefficients.


`3p + 4c = 40 \\ 10p + 4c = 68\ (multiplied\ both\ sides\ by\ 2)`

Then get it alone on one side.


`4c = 40-3p \\ 4c = 48-10p`

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


`40-3p = 68-10p \\ 40+7p = 68 \\ 7p = 28 \\ \boxed{p = 4}`

We can then use
`p = 4` in an earlier equation to find
`c`.


`5p + 2c = 34 \\ 5*4 + 2c = 34 \\ 20 + 2c = 34 \\ 2c = 14 \\ \boxed{c=7}`