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To determine the cost of each turkey sandwich without the delivery fee, we set up the following equations based on the information provided:

1. $ C \times 4 + D = 33 $   (Cost for 4 sandwiches plus delivery fee)
2. $ C \times 8 + D = 61 $   (Cost for 8 sandwiches plus delivery fee)

Here, $ C $ represents the cost of each turkey sandwich, and $ D $ represents the delivery fee.

We can solve this system of equations by elimination or substitution. Let's solve it by elimination to find $ C $ and $ D $.

### Steps:
1. Multiply the first equation by 2 to balance the equation with the second in terms of $ D $:
   \[ 2(C \times 4 + D) = 2 \times 33 \]
   \[ 8C + 2D = 66 \]

2. Subtract the first modified equation from the second equation:
   \[ (8C + D) - (8C + 2D) = 61 - 66 \]
   \[ -D = -5 \]
   \[ D = 5 \]   (Delivery fee)

3. Substitute $ D = 5 $ into the first original equation:
   \[ 4C + 5 = 33 \]
   \[ 4C = 28 \]
   \[ C = 7 \]   (Cost of each turkey sandwich)

Thus, each turkey sandwich costs $ \$7 $ excluding the delivery fee.

Would you like more details on these calculations or do you have any other questions? Here are some related topics you might find interesting:
1. What would the cost be for different numbers of sandwiches?
2. How would the equations change if the delivery fee varied with the number of sandwiches?
3. How can we graph these equations to visualize the solution?
4. Can this method be used for other types of problems with different fee structures?
5. What if the sandwich store offers a discount after a certain number of sandwiches are ordered?

Tip: When solving systems of equations, always look for opportunities to simplify or manipulate one equation to make the variables easier to isolate.

A sandwich store charges a delivery fee to bring lunch to an office building. One office pays $33 for 4 turkey sandwiches. Another office pays $61 for 8 turkey sandwiches. How much does each turkey sandwich cost (not including the cost of delivery)?

Learn how to determine the cost of each turkey sandwich and the delivery fee by solving a system of linear equations. Suitable for Grades 6-8.

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