In a survey conducted by Helena, a financial consultant, it was revealed of her 426 clients
287 own stocks.
188 own bonds.
184 own mutual funds.
118 own both stocks and bonds.
99 own both stocks and mutual funds.
94 own both bonds and mutual funds.
How many of Helena's clients own stocks, bonds, and mutual funds?
Did you draw the three intersection Circles?
It is the intersection place of all three that you are looking for.
Thus
426 which is the total number enrolled is equal to all the partial segment combined
426 = 287 - 99 - 118 - 94 + 184 + x
now solve for x
I got 160 for X and subtracted that from 426, getting 266 which is incorrect. I don't understand the answer.
To find out how many of Helena's clients own stocks, bonds, and mutual funds, we will use a technique called the inclusion-exclusion principle.
Step 1: Find the number of clients who own both stocks and bonds.
From the survey data, we know that 118 clients own both stocks and bonds.
Step 2: Find the number of clients who own both stocks and mutual funds.
From the survey data, we know that 99 clients own both stocks and mutual funds.
Step 3: Find the number of clients who own both bonds and mutual funds.
From the survey data, we know that 94 clients own both bonds and mutual funds.
Now, to calculate the number of clients who own all three (stocks, bonds, and mutual funds), we will use the inclusion-exclusion principle.
Step 4: Subtract the number of clients who own both stocks and bonds from the total number of clients who own stocks:
287 - 118 = 169
Step 5: Subtract the number of clients who own both stocks and mutual funds from the total number of clients who own stocks:
169 - 99 = 70
Step 6: Subtract the number of clients who own both bonds and mutual funds from the total number of clients who own bonds:
188 - 94 = 94
Step 7: Subtract the number obtained in Step 6 from the number obtained in Step 5 to get the number of clients who own all three:
70 - 94 = -24
The result is -24, which seems incorrect because we can't have a negative number of clients. It's possible that there was an error in the survey data or in the information provided.
Unfortunately, based on the given information, we cannot accurately determine the number of clients who own stocks, bonds, and mutual funds.