At a certain toy store, tiny stuffed pandas cost `$3.50` and giant stuffed pandas cost `$14.` If the store sold 29 panda toys and made `$217` inn revenue in one week how many tiny stuffed pandas and giant stuffed pandas were sold ?

Options

A. 18 tiny stuffed pandas, 11 gaint stuffed pandas
B. 11 tiny stuffed pandas, 18 gaint stuffed pandas
C. 12 tiny stuffed pandas, 17 giant stuffed pandas
D. 18 tiny stuffed pandas, 13 giant stuffed pandas

Explanation

To solve the problem of how many tiny stuffed pandas and giant stuffed pandas were sold, we can set up a system of linear equations based on the information provided.

### Step 1: Define Variables
Let:
- \( T \) = number of tiny stuffed pandas sold
- \( G \) = number of giant stuffed pandas sold

### Step 2: Set Up the Equations
From the problem, we have two key pieces of information:
1. The total number of pandas sold is 29.
2. The total revenue from selling the pandas is $217.

This gives us the following equations:
1. \( T + G = 29 \) (Equation 1)
2. \( 3.5T + 14G = 217 \) (Equation 2)

### Step 3: Solve the First Equation for One Variable
We can express \( G \) in terms of \( T \) using Equation 1:
\[ G = 29 - T \]

### Step 4: Substitute into the Second Equation
Now, substitute \( G \) in Equation 2:
\[ 3.5T + 14(29 - T) = 217 \]
Expanding this gives:
\[ 3.5T + 406 - 14T = 217 \]

### Step 5: Combine Like Terms
Combine the terms involving \( T \):
\[ -10.5T + 406 = 217 \]

### Step 6: Isolate \( T \)
Subtract 406 from both sides:
\[ -10.5T = 217 - 406 \]
\[ -10.5T = -189 \]
Now, divide by -10.5:
\[ T = \frac{-189}{-10.5} = 18 \]

### Step 7: Find \( G \)
Now that we have \( T \), we can find \( G \):
\[ G = 29 - T = 29 - 18 = 11 \]

### Step 8: Conclusion
Thus, the store sold:
- **18 tiny stuffed pandas**
- **11 giant stuffed pandas**

### Summary of the Solution
- Tiny stuffed pandas sold: \( T = 18 \)
- Giant stuffed pandas sold: \( G = 11 \)