Question
In a loan database, there are 27 loans to clients with 8 years of business experience. Also,
there are 29 loans made to clients with a Graduate education. In the database there are 52
loans to clients with 8 years of experience or who have a Graduate education. How many
loans were made to clients with a Graduate education who also had 8 years of experience?
Answer
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there are 29 loans made to clients with a Graduate education. In the database there are 52
loans to clients with 8 years of experience or who have a Graduate education. How many
loans were made to clients with a Graduate education who also had 8 years of experience?
Answer
Question Help:
Calculator
Ask by Stanley Ball. in the United States
Mar 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
There are 4 loans to clients with both a Graduate education and 8 years of experience.
Solution
We start with the formula for the union of two sets:
where:
-
(loans with 8 years of experience), -
(loans to clients with a Graduate education), -
(loans to clients with 8 years of experience or a Graduate education).
Substituting the given values:
Simplify the sum:
Solve for
Thus, the number of loans to clients with both a Graduate education and 8 years of experience is:
Answered by UpStudy AI and reviewed by a Professional Tutor
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Explain 
Simplify this solution The Deep Dive
To find the number of loans made to clients with both 8 years of experience and a Graduate education, we can use the principle of inclusion-exclusion.
Let:
-
be the loans to clients with 8 years of experience = 27 -
be the loans to clients with Graduate education = 29 -
be the loans to clients with either 8 years of experience or a Graduate education = 52
Using the formula:
Where
Plugging in our values:
Thus, the number of loans made to clients with a Graduate education who also had 8 years of experience is
