On sunday, a local hamburger shop sold a combined total of 368 hamburgers and cheeseburgers. the number of cheeseburgers sold was three times the number of hamburgers sold. how many hamburgers were sold on sunday?

This word problem requires a system. First though, what are we trying to find? We are trying to find how many hamburgers were sold on Sunday. That will be represented by x. Now we can find the first equation for the system:

x + y = 368

The next step is to find the second equation for the system. In the problem, it mentions that the number of cheeseburgers sold was three times the number of hamburgers sold. Based on this, we can get the second equation for the system:

x = 3y

Now here is the completed system:

x + y = 368
x = 3y

When we look at this system, we can see that x is equal to 3y. Now we just plug that in to make one equation with one variable:

3y + y = 368

Simplified, this would be:

4y = 368

Now we just undo the multiplication by dividing both sides by 4. This will answer our equation:

y = 92

If we plug in 92 for y into the simplest of the two equations in our system, we end up with this:

x + 92 = 368

Now we undo the addition by subtracting 92 from both sides:

x = 276

Now we see that our final answer is:
"276 hamburgers were sold on Sunday."