Final answer:
To determine the number of hamburgers sold at the local hamburger shop on Friday, we use a system of equations and find that 275 hamburgers were sold.
Step-by-step explanation:
The local hamburger shop sold a combined total of 621 hamburgers and cheeseburgers on Friday. It is given that there were 71 more cheeseburgers sold than hamburgers. To find out how many hamburgers were sold, we need to set up a system of equations.
Let H represent the number of hamburgers, and C represent the number of cheeseburgers. Since there were 71 more cheeseburgers than hamburgers, we can express this as C = H + 71. The total number of burgers sold was 621, so we have another equation: H + C = 621.
Now we can substitute the first equation into the second one: H + (H + 71) = 621. This simplifies to 2H + 71 = 621. Subtracting 71 from both sides gives us 2H = 550. Dividing both sides by 2, we find that H = 275. Therefore, the hamburger shop sold 275 hamburgers on Friday.