A store is selling two mixtures of coffee beans in one-pound bags. The first mixture has 12 ounces of Sumatra combined with 4 ounces of Celebes Kalossi, and costs $15. The second mixture has 4 ounces of Sumatra and 12 ounces of Celebes Kalossi, and costs $21. How much does one ounce of Sumatra and one ounce of Celebes Kalossi cost?

Select one:
a. $1.65 for Sumatra and $1.20 for Celebes Kalossi
b. $0.75 for Sumatra and $1.50 for Celebes Kalossi
c. There is no solution.
d. $1.50 for Sumatra and $0.75 for Celebes Kalossi

To solve this problem, we'll set up a system of equations.

Let's denote the cost of 1 ounce of Sumatra coffee as "s" and the cost of 1 ounce of Celebes Kalossi coffee as "c".

From the information given, we can write the following equations:

Equation 1: 12s + 4c = 15
Equation 2: 4s + 12c = 21

To solve this system of equations, we'll use the method of substitution.

From Equation 1, we can solve for s in terms of c:

12s + 4c = 15
12s = 15 - 4c
s = (15 - 4c)/12

Now, we'll substitute this value of s into Equation 2:

4s + 12c = 21
4((15 - 4c)/12) + 12c = 21
(60 - 16c)/12 + 12c = 21
(60 - 16c + 12c^2)/12 = 21

Simplifying further:

60 - 16c + 12c^2 = 252
12c^2 - 16c + 192 = 0
3c^2 - 4c + 48 = 0

Unfortunately, this quadratic equation does not have real solutions. Thus, the answer is c. There is no solution.

To find the cost per ounce of Sumatra and Celebes Kalossi, we can set up a system of equations.

Let's assume the cost per ounce of Sumatra is x, and the cost per ounce of Celebes Kalossi is y.

For the first mixture:
12 ounces of Sumatra at x dollars per ounce
4 ounces of Celebes Kalossi at y dollars per ounce

So, the cost of the first mixture would be: 12x + 4y = 15

For the second mixture:
4 ounces of Sumatra at x dollars per ounce
12 ounces of Celebes Kalossi at y dollars per ounce

So, the cost of the second mixture would be: 4x + 12y = 21

Now, we have a system of two equations:
12x + 4y = 15
4x + 12y = 21

We can solve this system of equations to find the values of x and y.

Multiplying the first equation by 3 and the second equation by (-1), we get:

36x + 12y = 45
-4x - 12y = -21

Adding these two equations together eliminates the y term:

32x = 24

Dividing both sides by 32, we find:
x = 0.75

Substituting the value of x into one of the original equations, we can solve for y:

12(0.75) + 4y = 15
9 + 4y = 15
4y = 6
y = 1.5

Therefore, one ounce of Sumatra costs $0.75, and one ounce of Celebes Kalossi costs $1.50.

Therefore, the correct answer is option d. $1.50 for Sumatra and $0.75 for Celebes Kalossi.

12s+4c = 15

4s+12c = 21

now just solve for s and c.