Please Solve

Question

A dealer sold 372 cars. Every car was either sold to a first-time buyer or sold with a 5-year service contract. Some were both. If 212 cars went to first-time buyers and 249 were sold with service contracts, how many first-time buyers purchased the service contract?

Answer 1

We use the results from set theory to do this. Drawing a Ven diagram with 2 intersecting set would help understand better.

 

Let A = car sold to first time buyer 

Let B = car sold with 5yr contract

 So A U B ( ie union of A and B ) will be car sold to a first time buyer or with 5yr contract

and A ∩ B will be car sold to a first time buyer with a 5 yr contract

 

Given 372 cars sold in all so A U B =  372

A = 212 

B = 249 

 

we need to find A ∩ B 

 

We know A U B =  A + B - ( A ∩ B )

so, 372 = 212 + 249 - A∩ B 

or A ∩ B  = 89

 

so 89 people who bought the car were first time buyers and took the contractt

 

 

Answer 2

If there was no overlap, then 212 + 249 = 461 cars were sold. But it says 372 cars were sold. So there must be 461 - 372 = 89 cars with overlap between first-time buyers and service contracts.