Question

The Coffee Counter charges ​$8 per pound for Kenyan French Roast coffee and ​$7 per pound for Sumatran coffee.

How much of each type should be used to make a 20 pound blend that sells for ​$7.30 per​ pound?

Answer 1

To create a 20-pound coffee blend priced at $7.30 per pound, use 6 pounds of Kenyan French Roast coffee and 14 pounds of Sumatran coffee by solving the system of linear equations based on the given prices.

Step-by-step explanation:

To determine how much of each type of coffee should be used to make a 20-pound blend that sells for $7.30 per pound, we can set up a system of equations based on the given prices and weights.

Let x be the amount of Kenyan French Roast coffee at $8 per pound, and y be the amount of Sumatran coffee at $7 per pound. We have two equations:

• The total weight of the blend: x + y = 20 pounds
• The total cost of the blend: 8x + 7y = 7.30 × 20

Solving the system of equations, we can find:

1. x + y = 20 (Equation 1)
2. 8x + 7y = 146 (Equation 2, because 7.30 × 20 = 146)

Next, we solve for y in Equation 1:

y = 20 - x

We substitute the value of y into Equation 2:

8x + 7(20 - x) = 146

Expanding and simplifying gives us:

8x + 140 - 7x = 146

x = 146 - 140

x = 6 pounds of Kenyan French Roast coffee

Then we use x to find y:

y = 20 - 6 = 14 pounds of Sumatran coffee

Therefore, to make the 20-pound coffee blend priced at $7.30 per pound, you'd need 6 pounds of Kenyan French Roast coffee and 14 pounds of Sumatran coffee.

Answer 2

Kenyan French Roast coffee x=6

Sumatran coffee y=14

Step-by-step explanation:

x+y=20 blend coffee

8x+7y=7.3(20) selling price

x+y=20 ⇒ x=20-y

substitute in the equation:

8x+7y=7.3(20)

8(20-y)+7y=7.3(20) for 20 pound blend

160-8y+7y=146

-y=146-160

y=14 pond

x+y=20

x=20-14=6

check : 14*7+6(8)=146/7.3=20 pound