Question

Sylvia wants to mix 100 pounds of Breakfast Blend coffee that will send for $25 per pound. She is using two types of coffee to create the mixture. Kona coffee sells for $51 per pound and Columbian coffee sells for $11 per pound. How many pounds of each type of coffee should Sylvia use

Answer 1

To create a 100-pound Breakfast Blend coffee selling at $25 per pound using Kona coffee at $51 per pound and Columbian coffee at $11 per pound, Sylvia should mix 35 pounds of Kona coffee with 65 pounds of Columbian coffee.

Step-by-step explanation:

Sylvia wants to mix Kona coffee and Columbian coffee to create 100 pounds of Breakfast Blend coffee that will sell for $25 per pound. To solve this, we can set up a system of equations based on the total weight and total cost of the mixture.

Let x be the amount of Kona coffee (which sells for $51 per pound), and y be the amount of Columbian coffee (which sells for $11 per pound). We have two equations:

• The sum of the weights of the coffees must be 100 pounds: x + y = 100.
• The total cost of the coffees in the mixture must equal 100 pounds at $25 per pound: 51x + 11y = 100 × 25.

We can solve this system using substitution or elimination. I'll use the elimination method here:

1. Multiply the first equation by 11 to set up the elimination with the second equation: 11x + 11y = 1100.
2. Subtract this from the second cost equation: (51x + 11y) - (11x + 11y) = 2500 - 1100.
3. This simplifies to 40x = 1400, which we can solve to find x = 35.
4. Substitute x into the first equation to find y: 35 + y = 100.
5. This gives us y = 65.

Therefore, Sylvia should use 35 pounds of Kona coffee and 65 pounds of Columbian coffee to create the Breakfast Blend.

Answer 2

Answer: Sylvia should use 35 pounds of Kona coffee and 65 pounds of Columbian coffee

Step-by-step explanation:

Let x represent the number of pounds of Kona coffee that Sylvia should use.

Let y represent the number of pounds of Columbian coffee that Sylvia should use.

Sylvia wants to mix 100 pounds of Breakfast Blend coffee. This means that

x + y = 100

She is using two types of coffee to create the mixture. Kona coffee sells for $51 per pound and Columbian coffee sells for $11 per pound and the mixture would sell for $25 per pound.

This means that

51x + 11y = 2500 - - - - - - - - 1

Substituting x = 100 - y into equation 1, it becomes

51(100 - y) + 11y = 2500

5100 - 51y + 11y = 2500

- 51y + 11y = 2500 - 5100

- 40y = - 2600

y = - 2600/-40

y = 65

x = 100 - y

x = 100 - 65 = 35