A local hamburger shop sold a combined total of 600 hamburgers and cheeseburgers on Saturday. There were 50 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Saturday?

Let the number of hamburgers sold be denoted by $ h $ and the number of cheeseburgers sold be denoted by $ c $.

We are given two key pieces of information:
1. The total number of hamburgers and cheeseburgers sold is 600:
   \[
   h + c = 600
   \]
2. There were 50 fewer cheeseburgers sold than hamburgers:
   \[
   c = h - 50
   \]

Now, substitute the second equation into the first equation:
\[
h + (h - 50) = 600
\]
Simplify the equation:
\[
2h - 50 = 600
\]
Add 50 to both sides:
\[
2h = 650
\]
Now, divide by 2:
\[
h = 325
\]

Thus, the number of hamburgers sold is $ 325 $.

If you want to check this, the number of cheeseburgers sold would be:
\[
c = h - 50 = 325 - 50 = 275
\]
And the total is:
\[
325 + 275 = 600
\]
which is correct.

So, the shop sold **325 hamburgers** on Saturday.

Do you want any more details or have any questions?

Here are 5 related questions:
1. How many cheeseburgers were sold on Saturday?
2. If the shop sells hamburgers at $5 each, how much did it earn from hamburgers on Saturday?
3. What percentage of the total sales were hamburgers?
4. If the shop sold 700 items the next day, with the same 50 fewer cheeseburgers than hamburgers, how many of each were sold?
5. What would happen if 100 more cheeseburgers were sold than hamburgers?

**Tip:** Always check your final result by plugging values back into the original equations!

Learn how to solve a system of linear equations where a shop sold 600 hamburgers and cheeseburgers, with 50 fewer cheeseburgers than hamburgers. This step-by-step solution uses algebraic techniques suitable for students in Grades 6-8.

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