Arthur has blended coffee worth 95 pesos per kilogram with coffee worth 115 pesos per kilogram to make 50 kilograms of coffee sold at 107 pesos per kilogram. How many kilograms of each kind did she blend

Let's use the method of weighted averages to solve this.

Let:
- \( x \) = kilograms of 95-peso coffee.
- \( 50 - x \) = kilograms of 115-peso coffee.

We know that the total weight of the blend is 50 kilograms, and the price of the blend is 107 pesos per kilogram. The equation for the total cost of the blend can be set up as follows:

\[
95x + 115(50 - x) = 107 \times 50
\]

### Step 1: Simplify the equation
First, calculate the total value on the right-hand side:

\[
107 \times 50 = 5350
\]

Now substitute this into the equation:

\[
95x + 115(50 - x) = 5350
\]

### Step 2: Distribute and combine like terms
Distribute the 115:

\[
95x + 5750 - 115x = 5350
\]

Now combine the \( x \)-terms:

\[
-20x + 5750 = 5350
\]

### Step 3: Solve for \( x \)
Subtract 5750 from both sides:

\[
-20x = 5350 - 5750
\]

\[
-20x = -400
\]

Now divide by -20:

\[
x = \frac{-400}{-20} = 20
\]

### Step 4: Find the amount of the 115-peso coffee
Since \( x = 20 \), the amount of the 95-peso coffee is 20 kilograms. The amount of the 115-peso coffee is:

\[
50 - x = 50 - 20 = 30 \, \text{kilograms}
\]

### Conclusion:
Arthur blended:
- 20 kilograms of 95-peso coffee,
- 30 kilograms of 115-peso coffee.

Would you like more details or have any questions?

Here are 5 related questions to think about:
1. How would the blend change if the target price was 110 pesos per kilogram?
2. What if Arthur wanted to blend 60 kilograms instead of 50? How would the amounts change?
3. How do we interpret this problem using the concept of the weighted average?
4. Can you solve the problem graphically by plotting costs vs. amounts?
5. How would the solution change if the cost per kilogram of the two coffees was closer together?

**Tip:** In mixture problems, the key is to balance both the quantity and the price to find the unknown values.

Arthur has blended coffee worth 95 pesos per kilogram with coffee worth 115 pesos per kilogram to make 50 kilograms of coffee sold at 107 pesos per kilogram. How many kilograms of each kind did she blend?

Discover how to solve a weighted average mixture problem where Arthur blends 95-peso and 115-peso coffee to make a 50-kilogram mixture at 107 pesos per kilogram. This step-by-step solution involves key algebraic concepts and linear equations. Perfect for students in Grades 8-10.

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