In a loan database, there are 60 loans to clients with 18 years of business experience. Also, there are 23 loans made to clients with a High School education. In the database there are 68 loans to clients with 18 years of experience or who have a High School education. How many loans were made to clients with a High School education who also had 18 years of experience?

Just make the usual Venn diagram. The number is

60+23-68 = 15

Thanks Steve

To find the number of loans made to clients with a High School education who also had 18 years of experience, we need to subtract the number of loans made to clients with 18 years of experience alone from the total number of loans made to clients with both 18 years of experience and High School education.

Let's break down the information given:

Number of loans to clients with 18 years of experience = 60
Number of loans to clients with a High School education = 23
Total number of loans to clients with 18 years of experience or High School education = 68

To find the number of loans made to clients with 18 years of experience and High School education, we can use the principle of inclusion and exclusion.

Step 1: Calculate the total number of loans made to clients with either 18 years of experience or High School education.

Total = Loans with 18 years of experience + Loans with High School education - Loans with both 18 years of experience and High School education
Total = 60 + 23 - Loans with both 18 years of experience and High School education

Now, we can substitute the value of the total number of loans made to clients with 18 years of experience or High School education, which is given as 68.

68 = 60 + 23 - Loans with both 18 years of experience and High School education

Step 2: Rearrange the equation to isolate the unknown number of loans with both 18 years of experience and High School education.

Loans with both 18 years of experience and High School education = 60 + 23 - 68
Loans with both 18 years of experience and High School education = 83 - 68
Loans with both 18 years of experience and High School education = 15

Therefore, there were 15 loans made to clients with a High School education who also had 18 years of experience.