A fabric store sells flannel and calico fabrics. Joan pays $25 for 3 yards of flannel and 4 yards of calico. Chris pays $11 for 1 yard of flannel and 2 yards of calico. What is the price of 1 yard of calico?

Options

A. $3
B. $4
C. $5
D. $6

Answer

To solve the problem, we need to set up a system of equations based on the information given about the purchases made by Joan and Chris.

### Step 1: Define Variables
Let:
- \( x \) = price of 1 yard of flannel
- \( y \) = price of 1 yard of calico

### Step 2: Set Up Equations
From the information provided:
1. Joan pays $25 for 3 yards of flannel and 4 yards of calico:
\[ 3x + 4y = 25 \quad \text{(Equation 1)} \]
2. Chris pays $11 for 1 yard of flannel and 2 yards of calico:
\[ x + 2y = 11 \quad \text{(Equation 2)} \]

### Step 3: Solve Equation 2 for \( x \)
We can express \( x \) in terms of \( y \) using Equation 2:
\[ x = 11 - 2y \quad \text{(Substituting for \( x \))} \]

### Step 4: Substitute \( x \) in Equation 1
Now substitute the expression for \( x \) into Equation 1:
\[ 3(11 - 2y) + 4y = 25 \]

### Step 5: Expand and Simplify
Expanding the equation:
\[ 33 - 6y + 4y = 25 \]
Combine like terms:
\[ 33 - 2y = 25 \]

### Step 6: Isolate \( y \)
Now, isolate \( y \):
\[ 33 - 25 = 2y \]
\[ 8 = 2y \]
Dividing both sides by 2 gives:
\[ y = 4 \]

### Conclusion
The price of 1 yard of calico is \( \boxed{4} \) dollars.

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