Question

Of the 50 researchers in a workgroup, 40 percent will be assigned to Team A and the remaining 60 percent to Team B. However, 70 percent of the researchers prefer Team A and 30 percent prefer Team B. What is the lowest possible number of researchers who will NOT be assigned to the team they prefer?

Answer 1

The lowest possible number of researchers who will NOT be assigned to the team they prefer is 15.

How did we get this value?

Let's start by finding out how many researchers will be assigned to each team based on the given percentages.

Total number of researchers = 50

Team A (40%): 0.4 * 50 = 20 researchers

Team B (60%): 0.6 * 50 = 30 researchers

Now, let's determine the number of researchers who prefer each team.

Team A (70%): 0.7 * 50 = 35 researchers

Team B (30%): 0.3 * 50 = 15 researchers

Now, we need to minimize the number of researchers who will NOT be assigned to the team they prefer. We can achieve this by making sure that as many researchers as possible get assigned to their preferred team.

In this case, the 30 researchers who prefer Team B will all be assigned to Team B, but only 20 researchers will be assigned to Team A. Therefore, 15 researchers who prefer Team A will not get their preferred assignment.

So, the lowest possible number of researchers who will NOT be assigned to the team they prefer is 15.

Answer 2

The lowest possible number of researchers who will not be assigned to the team they prefer is:

- 15 researchers.

Step-by-step explanation:

The operation can be solved in the next form:

The number of researchers: 50.

Team A members: 40% = 20 researchers.

Team B members: 60% = 30 researchers.

Researchers that prefer team A: 70% = 35.

Researchers that prefer team B: 30% = 15.

Assuming that all the members in team A, 20 researchers, prefer that team and the researchers that prefer team B are in it, we must do a subtraction:

Researchers that prefer the Team A - Team A members = 35 - 20 = 15 researchers.