Morgan runs a farm stand that sells apples and blueberries. Yesterday Morgan sold 20 pounds of apples and 50 pounds of blueberries for a total revenue of $160. Today she sold 38 pounds of apples and 10 pounds of blueberries for a total revenue of $134. Determine the price of each pound of apples and the price of each pound of blueberries.

To determine the price per pound of apples and blueberries, we can set up a system of equations based on the given information.

Let:
- $ x $ be the price per pound of apples,
- $ y $ be the price per pound of blueberries.

From the problem, we can form two equations:

1. From yesterday's sales:
   \[
   20x + 50y = 160
   \]
   (20 pounds of apples and 50 pounds of blueberries for a total of $160)

2. From today's sales:
   \[
   38x + 10y = 134
   \]
   (38 pounds of apples and 10 pounds of blueberries for a total of $134)

Now, we will solve this system of equations to find $ x $ and $ y $.

### Step 1: Solve one equation for one variable
We can solve one of the equations for one variable and substitute into the other. Let's solve the second equation for $ y $:
\[
38x + 10y = 134 \quad \Rightarrow \quad 10y = 134 - 38x \quad \Rightarrow \quad y = \frac{134 - 38x}{10}
\]

### Step 2: Substitute into the first equation
Substitute the expression for $ y $ into the first equation:
\[
20x + 50\left(\frac{134 - 38x}{10}\right) = 160
\]
Simplify the equation:
\[
20x + 5(134 - 38x) = 160
\]
\[
20x + 670 - 190x = 160
\]
\[
-170x + 670 = 160
\]
### Step 3: Solve for $ x $
\[
-170x = 160 - 670
\]
\[
-170x = -510
\]
\[
x = \frac{-510}{-170} = 3
\]
So, the price per pound of apples is $ x = 3 $ dollars.

### Step 4: Solve for $ y $
Substitute $ x = 3 $ into the expression for $ y $:
\[
y = \frac{134 - 38(3)}{10} = \frac{134 - 114}{10} = \frac{20}{10} = 2
\]
So, the price per pound of blueberries is $ y = 2 $ dollars.

### Final Answer:
- The price per pound of apples is **$3**.
- The price per pound of blueberries is **$2**.

Would you like further details or have any questions?

---

Here are 5 related questions to explore:

1. What would the revenue be if Morgan sold 15 pounds of apples and 30 pounds of blueberries tomorrow?
2. How would the price change if Morgan decided to increase the price of blueberries by 50%?
3. If Morgan sold only apples tomorrow, how many pounds would she need to sell to make $150?
4. How does the system of equations change if she gives a discount on both items?
5. Could Morgan sell different proportions of apples and blueberries and still make the same revenue? How?

**Tip:** For solving systems of equations, substitution and elimination methods are often interchangeable depending on the complexity of the problem.

Determine the price per pound of apples and blueberries using a system of linear equations. Morgan sold different quantities of apples and blueberries on two separate days, generating different revenues. Solve using algebra and substitution methods. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation