At a hockey game, a vender sold a combined total of  sodas and hot dogs. The number of sodas sold was  more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.

Let's define:

- \( h \) as the number of hot dogs sold.
- \( s \) as the number of sodas sold.

We are given two pieces of information:
1. The total number of sodas and hot dogs sold is 100. This gives us the equation:
   \[
   h + s = 100
   \]
2. The number of sodas sold is 10 more than the number of hot dogs sold. This gives us the second equation:
   \[
   s = h + 10
   \]

Now, we can solve these equations step by step.

### Step 1: Substitute the second equation into the first
Substitute \( s = h + 10 \) into \( h + s = 100 \):
\[
h + (h + 10) = 100
\]
Simplify the equation:
\[
2h + 10 = 100
\]
### Step 2: Solve for \( h \)
Subtract 10 from both sides:
\[
2h = 90
\]
Divide by 2:
\[
h = 45
\]
So, 45 hot dogs were sold.

### Step 3: Find \( s \)
Now, substitute \( h = 45 \) into \( s = h + 10 \):
\[
s = 45 + 10 = 55
\]
So, 55 sodas were sold.

### Final Answer:
- Number of hot dogs sold: 45
- Number of sodas sold: 55

Would you like further details on this problem or have any questions?

Here are 5 related questions for practice:
1. What if the total sales were 200 and sodas were 20 more than hot dogs?
2. If sodas were 5 fewer than hot dogs, how many of each would be sold?
3. What if the total sales were 120 and sodas were double the number of hot dogs?
4. How would you solve this problem if the number of hot dogs was unknown but sodas were 15 more?
5. If sodas were 3 times the number of hot dogs, what would the sales be?

**Tip:** When solving systems of equations, substitution is a powerful method to simplify and solve them efficiently.

At a hockey game, a vendor sold a combined total of sodas and hot dogs. The number of sodas sold was 10 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.

Learn how to solve a system of linear equations to find the number of sodas and hot dogs sold. The problem involves key algebraic concepts and uses substitution to solve a real-world problem suitable for students in Grades 6-8.

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