Question

Moonbucks Coffee Company sells a mixture with 12 ounces of Robusta coffee beans and 6 ounces of Arabica coffee beans for $12.30. They sell a mixture with 10 ounces of Robusta and 4 ounces of Arabica for $9.62. What is the price per ounce of each type of coffee bean?

Say what your variables represent, and set up the system of equations. x = _____

Answer 1

The price per ounce of Robusta coffee beans is $0.87 and the price per ounce of Arabica coffee beans is $0.63.

Step-by-step explanation:

We can set up a system of equations based on the given information. Let x represent the price per ounce of Robusta coffee beans and y represent the price per ounce of Arabica coffee beans.

From the first mixture, we know that 12x + 6y = 12.30. From the second mixture, we know that 10x + 4y = 9.62.

To solve this system, we can use the method of substitution or elimination. Let's use substitution:

1. From the first equation, solve for x in terms of y: x = (12.30 - 6y) / 12
2. Substitute this value of x into the second equation: 10((12.30 - 6y) / 12) + 4y = 9.62
3. Simplify and solve for y: 123 - 60y + 48y = 115.44
4. Combine like terms: -12y = -7.56
5. Divide by -12: y = 0.63
6. Substitute this value of y back into the first equation to solve for x: x = (12.30 - 6(0.63)) / 12
7. Simplify and solve for x: x = 0.87

Therefore, the price per ounce of Robusta coffee beans is $0.87 and the price per ounce of Arabica coffee beans is $0.63.