Analyze the details below and answer the question.

There are 450 employees in a company who use three (A, B and C) different communication systems. The ratio of the total number of employees who use only system A, only system B, and only system C is 5 : 7 : 3 respectively. Employees who use all three systems are 50% of the employees who use only system B. The sum of the employees who use only system B and system C and those who use only system A and system B is 50. The number of employees who use only system A and system C is 30.

What is the difference between the number of employees who use only system B and the number of employees who use only system A & system B?

The correct answer is Can’t be determined.

Step-by-step Explanation:

Step 1: Define the given parameters using Venn diagram regions.
Let the three communication systems be A, B, and C.
Let:

• Employees using only system A = $a=5k$

• Employees using only system B = $b=7k$

• Employees using only system C = $c=3k$

• Employees using all three systems (A, B, and C) = $50\%\text{of}b=0.5\times 7k=3.5k$

• Employees using only system A and system B = $x_{AB}$

• Employees using only system B and system C = $x_{BC}$

• Employees using only system A and system C = $x_{AC}=30$

Step 2: Use the total count of employees to find constant $k$.
Given that the sum of employees who use only (B & C) and only (A & B) is 50:

${\mathrm{xstyle}}_{}{x}_{AB}+x_{BC}=50$

Assuming all 450 employees use at least one system, the total number of employees is:

$\text{Total}=a+b+c+x_{AB}+x_{BC}+x_{AC}+\text{All three}$

Substitute the known values into the equation:

$450=5k+7k+3k+50+30+3.5k$

$450=18.5k+80$

$370=18.5k$

$k=20$

Step 3: Calculate the number of employees who use only system B.
Number of employees who use only system B:

$b=7k=7\times 20=140$

Step 4: Analyze the required difference.
We are asked to find the difference between the number of employees who use only system B ($b=140$) and the number of employees who use only system A & B ($x_{AB}$).
The required difference is:

$\text{Difference}=140-x_{AB}$

However, we are only given the combined sum $x_{AB}+x_{BC}=50$. There is no individual value provided for $x_{AB}$ (it can be any valid integer value within the range $0\le x_{AB}\le 50$).

Since the specific value of $x_{AB}$ cannot be uniquely determined from the given information, the exact difference also cannot be determined.