A grocery store is running a sale on seasonal berries. During the sale , the store sells packages of blueberries for $4 each and packages of strawberries for $6 each. Kate purchased nine packages of fruit for her mother's dinner party for $40. How many packages of blueberries did she purchase ?

Options

A. 2
B. 4
C. 6
D. 7

Answer

To solve the problem, we need to set up a system of equations based on the information provided. Let's break it down step by step.

### Step 1: Define Variables
Let:
- \( x \) = number of packages of blueberries
- \( y \) = number of packages of strawberries

### Step 2: Set Up the Equations
From the problem, we know:
1. The total number of packages purchased is 9:
\[ x + y = 9 \quad \text{(Equation 1)} \]

2. The total cost of the packages is $40:
\[ 4x + 6y = 40 \quad \text{(Equation 2)} \]

### Step 3: Solve the First Equation for \( y \)
From Equation 1, we can express \( y \) in terms of \( x \):
\[ y = 9 - x \quad \text{(Substituting into Equation 1)} \]

### Step 4: Substitute \( y \) into the Second Equation
Now, substitute \( y \) in Equation 2:
\[ 4x + 6(9 - x) = 40 \]

### Step 5: Simplify the Equation
Distributing the 6:
\[ 4x + 54 - 6x = 40 \]
Combine like terms:
\[ -2x + 54 = 40 \]

### Step 6: Solve for \( x \)
Subtract 54 from both sides:
\[ -2x = 40 - 54 \]
\[ -2x = -14 \]
Now divide by -2:
\[ x = 7 \]

### Step 7: Find \( y \)
Now that we have \( x \), we can find \( y \):
\[ y = 9 - x = 9 - 7 = 2 \]

### Conclusion
Kate purchased **7 packages of blueberries**.

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