A store is selling two mixtures of coffee beans in one-pound bags. The first mixture has 12 ounces of Sumatra combined with 44 ounces of Celebes Kalossi, and costs $42. The second mixture has 44 ounces of Sumatra and 12ounces of Celebes Kalossi, and costs $30. How much does one ounce of Sumatra and one ounce of Celebes Kalossi cost?

Create 2 equations for the given problem

12s + 44c = 42

44s + 12c = 30

Take either equation and solve for either s or c.

12s + 44c = 42

12s = 42 - 44c

s = (42 - 44c) / 12

s = (21 - 22c) / 6

Substitute into 2nd equation

44s + 12c = 30

22 ((21 - 22c) / 3) + 12c = 30

22 (21 - 22c) + 36c = 90

-448c + 462 = 90

-448c = - 372

c = - 372/-448

c = 93/112

c = 0.83

Substitute into the 2nd equation

44s + 12c = 30

44s = 30 - 12c

s = (30 - 12 (93/112)) / 44

s = (30 - 279 / 28) / 44)

s = (30 - 9 27/28) / 44

s = 0.46

Prove

12s + 44c = 42

12 (0.46) + 44 (0.83) = 42

5.52 + 36.52 = 42

42.04 = 42

44s + 12c = 30

44 (0.46) + 12 (0.83) = 30

20.24 + 9.96 = 30.16

Assuming minor rounding issues this looks accurate.