Final answer:
By setting up an algebraic equation, we determine there were 76 vegetarians at the company's Thanksgiving dinner, based on the information that there were fifty-two more vegetarians than non-vegetarians and the total number of attendees was one hundred.
Step-by-step explanation:
To calculate how many vegetarians were at the company's Thanksgiving dinner, let's set up the problem using algebra. Let v represent the number of vegetarians, and let n represent the number of non-vegetarians. According to the problem, there are fifty-two more vegetarians than non-vegetarians, and the total number of people at the dinner is one hundred. So we have two expressions: v = n + 52 and v + n = 100.
Now we can substitute the first expression into the second one to solve for n. Replacing v with n + 52 in the second expression, we get n + 52 + n = 100. Combining like terms, we have 2n + 52 = 100. We can then subtract 52 from both sides of the equation to isolate the term with n, leading to 2n = 48. Dividing both sides by 2 gives us the number of non-vegetarians, n = 24.
Subsequently, to find the number of vegetarians, we plug the value of n into the first expression to get v = 24 + 52 = 76. Thus, there were 76 vegetarians at the dinner.