Question

A store is selling two mixtures of nuts in two-pound bags. The first mixture has 20 ounces of almonds combined with 12 ounces of cashews, and costs $23.16 The second mixture has 18 ounces of almonds and 14 ounces of cashews, and costs $22.86. How much does one ounce of almonds and one ounce of cashews cost?

Answer 1

One ounce of almonds is $0.78

One ounce of cashews is $0.63

Explanation:

Set up a system of equations where a is the price of one ounce of almonds and c is the price of one ounce of cashews:

20a + 12c = 23.16

18a + 14c = 22.86

Solve by elimination by multiplying the top equation by 7 and the bottom equation by -6:

140a + 84c = 162.12

-108a - 84c = -137.16

Add them together and solve:

32a = 24.96

a = 0.78

Now, plug in 0.78 for a and solve for c:

20a + 12c = 23.16

20(0.78) + 12c = 23.16

15.6 + 12c = 23.16

12c = 7.56

c = 0.63