In a loan database, there are 15 loans to clients with 9 years of business experience. Also, there are 60 loans made to clients with a College education. In the database there are 63 loans to clients with 9 years of experience or who have a College education. How many loans were made to clients with a College education who also had 9 years of experience?
15+60-x = 63
Thanks! Steve
To find the number of loans made to clients with a College education and 9 years of experience, we need to use the principle of inclusion-exclusion.
First, start with the total number of loans in the database, which is the sum of loans made to clients with 9 years of experience and loans made to clients with a College education. That is:
Total loans = Loans with 9 years of experience + Loans with College education
Given that there are 15 loans to clients with 9 years of experience and 60 loans to clients with a College education, we can write the equation as:
Total loans = 15 + 60
Next, we need to remember that we have double-counted the loans made to clients with both 9 years of experience and a College education. So, we need to subtract the number of loans made to these clients once, in order to avoid overcounting.
The equation to perform this subtraction is:
Total loans - Loans with 9 years of experience and College education = Loans with 9 years of experience or College education but not both
We know that there are a total of 63 loans made to clients with 9 years of experience or who have a College education. Therefore, we can substitute the values into the equation:
63 = Total loans - Loans with 9 years of experience and College education
Now, we rearrange the equation to isolate the number of loans made to clients with 9 years of experience and College education:
Loans with 9 years of experience and College education = Total loans - 63
Substituting the previously known values:
Loans with 9 years of experience and College education = 15 + 60 - 63
Loans with 9 years of experience and College education = 75 - 63
Finally, perform the subtraction to find the answer:
Loans with 9 years of experience and College education = 12
Therefore, the number of loans made to clients with a College education who also had 9 years of experience is 12.