(from an actuarial exam) a company offers a health insurance plan, a life insurance plan, and an investment insurance plan. an employee can have 0, 1, or 2 plans, but cannot have both life insurance and investment plans. you are given the following information: • 450 employees have at least one plan. • 330 employees have only one plan. • 320 employees have the health insurance plan. • 45 employees have only the life insurance plan. • there are 20 more employees that have both health and life plans than those that have both health and investment plans. how many people have the investment plan

Step-by-step explanation:

We can work with these values as a set value, and build a Venn Diagram from them.

I am going to say the set A are those that have the health insurance plan.

Set B are those that have the life insurance plan

Set C are those that have the investment plan.

We have that:

In which a is the number of employees that only have the health insurance plan, is the number of employees that have both the health and the life insurance plans, is the number of employees that have both the health insurance and the investment plans. and is the number of employees that have all three of those plans.

By the same logic, we have that:

The problem states that:

An employee cannot have both life insurance and investment plans. So:

45 employees have only the life insurance plan. So:

There are 20 more employees that have both health and life plans than those that have both health and investment plans

320 employees have the health insurance plan.

450 employees have at least one plan

330 employees have only one plan

How many people have the investment plan?

We have to find the value of C.

Now we solve:

Applying what we have

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The number of people that have the investment plan is:

135 people have the investment plan