The Coffee Counter charges ​$11.00 per pound for Kenyan French Roast coffee and ​$15.00 per pound for Sumatran coffee.

How much of each type should be used to make a 26 pound blend that sells for ​$13.00 per​ pound?

We can solve this problem by using a system of equations. Let:

- $ x $ be the number of pounds of Kenyan French Roast coffee.
- $ y $ be the number of pounds of Sumatran coffee.

We know the following:

1. The total weight of the blend is 26 pounds:
   \[
   x + y = 26
   \]

2. The cost of the blend should be $13.00 per pound, and the total cost of the blend is:
   \[
   11x + 15y = 13 \times 26 = 338
   \]

Now, we can solve this system of equations:

\[
x + y = 26
\]
\[
11x + 15y = 338
\]

### Step 1: Solve the first equation for $ y $:
\[
y = 26 - x
\]

### Step 2: Substitute $ y = 26 - x $ into the second equation:
\[
11x + 15(26 - x) = 338
\]
\[
11x + 390 - 15x = 338
\]
\[
-4x + 390 = 338
\]
\[
-4x = 338 - 390
\]
\[
-4x = -52
\]
\[
x = 13
\]

### Step 3: Substitute $ x = 13 $ back into $ y = 26 - x $:
\[
y = 26 - 13 = 13
\]

Thus, you should use **13 pounds of Kenyan French Roast coffee** and **13 pounds of Sumatran coffee** to make the blend.

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How would the solution change if the total blend weight were different?
2. What if the price per pound of one coffee increased by $2? How would that affect the blend proportions?
3. Can this problem be solved using matrix methods?
4. What if the desired blend price were lower, say $12 per pound?
5. How would you handle multiple types of coffee in a blend?

**Tip:** When solving systems of equations, substitution is often a simpler method when one equation can easily be solved for a variable.

The Coffee Counter charges ​$11.00 per pound for Kenyan French Roast coffee and ​$15.00 per pound for Sumatran coffee. How much of each type should be used to make a 26 pound blend that sells for ​$13.00 per​ pound?

Learn how to solve a system of equations to find how much Kenyan French Roast and Sumatran coffee should be blended to make 26 pounds at $13 per pound. This step-by-step guide covers algebraic concepts like linear equations and the substitution method, suitable for Grades 9-11.

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