A model train is made by connecting cars with possible lengths of 2 inches and 5 inches. what is the number of inches in the greatest impossible whole-number length of such a train?
To find the greatest impossible whole-number length of such a train, we need to use the Chicken McNugget theorem.
The Chicken McNugget theorem states that for two relatively prime positive integers, let's call them a and b, the largest integer that cannot be expressed as the sum of the multiples of a and b is given by ab - a - b.
In this case, the possible lengths of the train cars are 2 inches and 5 inches. The greatest common divisor (GCD) between 2 and 5 is 1, which means they are relatively prime.
To find the greatest impossible whole-number length, we can apply the Chicken McNugget theorem:
Greatest impossible length = (2)(5) - 2 - 5
= 10 - 2 - 5
= 3 inches
Therefore, the greatest impossible whole-number length of the train is 3 inches.