https://file.aiquickdraw.com/mathbot/file/17304832716954v9gnd1m.jpg

To solve this, let’s break down the information given:

1. **First Blend Composition and Cost:**
   - 4 lbs of Colombian coffee beans.
   - 6 lbs of Guatemalan coffee beans.
   - Total cost of this blend is $45.90.

   Let’s define:
   - $ x $ = price per pound of Colombian coffee beans
   - $ y $ = price per pound of Guatemalan coffee beans

   The equation for the cost of this blend is:
   \[
   4x + 6y = 45.90
   \]

2. **Second Blend Composition and Cost:**
   - Contains equal amounts of Colombian and Guatemalan coffee beans, totaling 10 lbs (so, 5 lbs each).
   - Total cost of this blend is $47.

   This gives us a second equation:
   \[
   5x + 5y = 47
   \]

### Solving the System of Equations
1. Simplify the second equation by dividing everything by 5:
   \[
   x + y = 9.4
   \]

2. Now we have the system:
   \[
   4x + 6y = 45.90
   \]
   \[
   x + y = 9.4
   \]

3. Solve for $ x $ in terms of $ y $ from the second equation:
   \[
   x = 9.4 - y
   \]

4. Substitute $ x = 9.4 - y $ into the first equation:
   \[
   4(9.4 - y) + 6y = 45.90
   \]
   \[
   37.6 - 4y + 6y = 45.90
   \]
   \[
   2y = 8.3
   \]
   \[
   y = 4.15
   \]

5. Substitute $ y = 4.15 $ back into $ x + y = 9.4 $:
   \[
   x + 4.15 = 9.4
   \]
   \[
   x = 5.25
   \]

### Answer
The price per pound of the Guatemalan coffee beans is **$4.15**.

---

Would you like further details on this solution, or have any questions?

Here are 5 related questions for further practice:
1. How would the cost change if we adjusted the blend ratios?
2. If the price of Colombian coffee beans increased, how would it affect the blend cost?
3. What if the blend ratio was reversed to 6 lbs Colombian and 4 lbs Guatemalan?
4. How would you find the price per pound if the second blend had unequal parts?
5. Can you set up a similar problem with different prices and quantities?

**Tip:** In problems with mixtures or blends, setting up a system of equations is key for solving price and quantity questions efficiently.

A coffee shop sells different blends of coffee. One blend is made by combining 4 lbs of Columbian and 6 lbs of Guatemalan coffee beans. This blend costs $45.90 to make. A second blend contains equal amounts of each, for a total of 10 lbs. This second blend costs $47. What is the price per pound of the Guatemalan coffee beans?

Solve a systems of equations problem involving coffee blends to find the price per pound of Guatemalan coffee beans. The problem provides weights and costs of two blends, using algebra to determine the price per pound. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation