Question

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 $32. The second mixture has 4 ounces of Sumatra and 12 ounces of Celebes Kalossi, and costs $40. How much does one ounce of Sumatra and one ounce of Celebes Kalossi cost?

Answer 1

To solve the problem, we set up two equations based on the given mixtures and costs. Using the elimination method, we determined the cost per ounce of Sumatra to be $1.75 and Celebes Kalossi to be $2.75.

Step-by-step explanation:

This is a classic algebra problem where we have two mixtures and we are trying to find out the price per ounce of two different types of coffee beans: Sumatra and Celebes Kalossi.

Let's define two variables for the prices per ounce:

• S = cost per ounce of Sumatra
• C = cost per ounce of Celebes Kalossi

Now, we set up our equations based on the information provided:

1. 12S + 4C = $32 (for the first mixture)
2. 4S + 12C = $40 (for the second mixture)

We can solve this system of equations using the substitution or elimination method. For simplicity, let's use the elimination method:

Multiplying the first equation by 3 and the second equation by 1 (to line up the 'C' terms) gives us:

• 36S + 12C = $96
• 4S + 12C = $40

Subtracting the second equation from the first, we get:

• 32S = $56

Dividing both sides by 32 gives us the price per ounce of Sumatra (S):

• S = $1.75

Using the value of S, plug it back into one of the original equations to find the price per ounce of Celebes Kalossi (C). Let's use the first equation:

• 12(1.75) + 4C = $32
• 21 + 4C = $32
• 4C = $11
• C = $2.75

Therefore, one ounce of Sumatra costs $1.75 and one ounce of Celebes Kalossi costs $2.75.

Answer 2

We let x as the cost of one ounce of Sumatra and y as the cost of one ounce of Celebes Kalossi. For mixture 1, we have 12x + 4y = 32 and for mixture b, we have 4x + 12y = 40

First, Multiply eq. 1 by 4
4(12x + 4y = 32)4 ⇒ 36x + 12y = 96

We now have
(36x + 12y = 96) – (4x + 12y = 40)
X = 1.75 ⇒ cost of one ounce of Sumatra

Substitute x to either equation to get the value of y
12(1.75) + 4y = 324
y = 32-21
4y = 11
Y = 2.75 ⇒ cost of one ounce of Celebes Kalossi