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The problem reads:

"Three orders are placed at a pizza shop. The small pizza, a liter of soda, and a salad cost $15; one small pizza, a liter of soda, and three salads cost $19; and three small pizzas, a liter of soda, and two salads cost $22. How much does each item cost?"

Let's define variables:
- Let the cost of a small pizza be $ p $.
- Let the cost of a liter of soda be $ s $.
- Let the cost of a salad be $ d $.

The problem gives us three equations:
1. $ p + s + d = 15 $
2. $ p + s + 3d = 19 $
3. $ 3p + s + 2d = 22 $

Now, we can solve this system of linear equations.

### Step 1: Subtract equation 1 from equation 2 to eliminate $ p $ and $ s $:
\[
(p + s + 3d) - (p + s + d) = 19 - 15
\]
\[
2d = 4 \quad \Rightarrow \quad d = 2
\]

### Step 2: Substitute $ d = 2 $ into equation 1:
\[
p + s + 2 = 15 \quad \Rightarrow \quad p + s = 13 \tag{4}
\]

### Step 3: Substitute $ d = 2 $ into equation 3:
\[
3p + s + 2(2) = 22 \quad \Rightarrow \quad 3p + s + 4 = 22 \quad \Rightarrow \quad 3p + s = 18 \tag{5}
\]

### Step 4: Subtract equation 4 from equation 5:
\[
(3p + s) - (p + s) = 18 - 13
\]
\[
2p = 5 \quad \Rightarrow \quad p = 2.5
\]

### Step 5: Substitute $ p = 2.5 $ into equation 4:
\[
2.5 + s = 13 \quad \Rightarrow \quad s = 13 - 2.5 \quad \Rightarrow \quad s = 10.5
\]

### Final Answer:
- The cost of a small pizza $ p $ is $2.50.
- The cost of a liter of soda $ s $ is $10.50.
- The cost of a salad $ d $ is $2.

Would you like more details, or do you have any other questions?

### Related Questions:
1. How can you check if the solution satisfies all the given equations?
2. What would happen if the prices were different? Can you solve a similar system with other values?
3. How can systems of linear equations be used in other real-life situations?
4. What methods can be used to solve systems of equations besides substitution?
5. How would the solution change if the problem had more variables or equations?

### Tip:
When solving systems of equations, always check your solution by substituting the values back into the original equations.

Three orders are placed at a pizza shop. The small pizza, a liter of soda, and a salad cost $15; one small pizza, a liter of soda, and three salads cost $19; and three small pizzas, a liter of soda, and two salads cost $22. How much does each item cost?

Learn how to solve a system of equations to find the cost of a pizza, a soda, and a salad. This problem involves algebraic concepts, such as linear equations and the substitution method, and is ideal for students in Grades 8-10.

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