Question

A profile of the investments owned by an agent’s clients follows: 228 own annuities. 220 own mutual funds. 98 own life insurance and mutual funds. 93 own annuities and mutual funds. 16 own annuities, mutual funds, and life insurance. 45 more clients own only life insurance than own only annuities. 290 own only one type of investment (i.e., annuity, mutual fund, or life insurance). Calculate the agent’s total number of clients.

Answer 1

Total number of clients =500

Explanation:

Refer to the Venn diagram for the pictorial representation.

Let x represent the number of clients for annuities only,

Then number of clients for life insurance only = x+45

Number of clients for annuities and mutual funds only = 93-16 = 77

Number of clients for life assurance and mutual funds only = 98-16 =82

Number of clients for mutual funds only = 220 -(77+16+82) =45

from the question 290 own only one type of investment.

x+x+45+45 =290

2x+90=290

2x=290-90

2x=200

`x=(200)/(2)`

x=100.

clients for annuities only = 100

clients for Life insurance only =x+45= 100+45=145

228 clients own annuities,

number of clients that own annuities and life assurance only = 228-(100+77+16)

=228-193

=35

Total number of clients = sum of all the spaces in the Venn diagram.

= 100+77+16+35+45+82+145

=500 clients