A store is selling two mixtures of nuts in 20-ounce bags. The first mixture has 15 ounces of peanuts combined with five ounces of cashews, and costs $6.00. The second mixture has five ounces of peanuts and 15 ounces of cashews, and costs $8.00. How much does one ounce of peanuts and one ounce of cashews cost?
Let's say the cost of one ounce of peanuts is p dollars, and the cost of one ounce of cashews is c dollars.
We'll first set up two equations based on what we know:
15p + 5c = 6 (equation 1)
5p + 15c = 8 (equation 2)
We can solve this system of equations by multiplying equation 1 by 3 and equation 2 by -1, so we get:
45p + 15c = 18 (equation 3)
-5p - 15c = -8 (equation 4)
Adding equation 3 and equation 4 eliminates the variable c, so we have:
45p + 15c - 5p - 15c = 18 - 8
40p = 10
p = 10/40
p = 1/4
Substituting this value back into equation 1, we get:
15(1/4) + 5c = 6
15/4 + 5c = 6
5c = 24/4 - 15/4
5c = 9/4
c = 9/4 * 1/5
c = 9/20
Therefore, one ounce of peanuts and one ounce of cashews cost $1/4 and $9/20, respectively.