Question 6:  A restaurant sold 350 less hotdogs than hamburgers.  Altogether, the restaurant sold 700 hotdogs and hamburgers.  How many of each did they sell? 

Let's define variables for the number of hotdogs and hamburgers sold:

- Let \( h \) represent the number of hotdogs sold.
- Let \( b \) represent the number of hamburgers sold.

From the problem, we have two key pieces of information:

1. The restaurant sold 350 fewer hotdogs than hamburgers, which gives us the equation:
   \[
   h = b - 350
   \]
   
2. The total number of hotdogs and hamburgers sold is 700, which gives us another equation:
   \[
   h + b = 700
   \]

### Solving the system of equations:
Substitute \( h = b - 350 \) from the first equation into the second equation:

\[
(b - 350) + b = 700
\]

Simplify the equation:

\[
2b - 350 = 700
\]

Add 350 to both sides:

\[
2b = 1050
\]

Divide by 2:

\[
b = 525
\]

Now, substitute \( b = 525 \) into the first equation to find \( h \):

\[
h = 525 - 350 = 175
\]

### Conclusion:
- The restaurant sold **175 hotdogs**.
- The restaurant sold **525 hamburgers**.

Would you like more details or have any questions?

Here are some related questions to explore:

1. If the total number of items sold increased to 900, with the same difference of 350, how many hotdogs and hamburgers were sold?
2. If the restaurant sold 700 items but the difference between hotdogs and hamburgers was 200, how would the numbers change?
3. What if the restaurant sold 1.5 times more hamburgers than hotdogs? How many of each were sold if the total is still 700?
4. How would the solution change if the number of hamburgers sold was unknown, but the number of hotdogs was given directly?
5. If hotdogs and hamburgers together made up 80% of the total sales, and the remaining were drinks, what was the total number of items sold?

**Tip:** When solving word problems, clearly define your variables and translate the problem into equations before solving!

A restaurant sold 350 fewer hotdogs than hamburgers. Altogether, the restaurant sold 700 hotdogs and hamburgers. How many of each did they sell?

Learn how to solve a system of linear equations with a real-world problem involving hotdogs and hamburgers. The restaurant sold 350 fewer hotdogs than hamburgers, and the total sold is 700. This problem demonstrates algebraic concepts and the substitution method, suitable for Grades 6-8.

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