A college student needs 15 classes that are worth a total of 40 credits in order to complete her degree. The college offers both 3-credit classes and 2-credit classes. How many 2-credit classes and 3-credit classes can the student take?

12 three credit classes and two 2 credits

249335 miles

Step-by-step explanation:

Let x be the number of miles the car has travelled.

The odometer can only tell us that x≡49335(mod 100000).

If we also know the value of c where x≡c(mod 7)and 0≤c<7 by the Chinese remainder theorem we know the congruence satisfied by x modulo 100000•7 = 700000.

As long as the car has been driven less that 700000 this uniquely determines the number of miles driven.

In particular, we easily see that if x≡6 (mod 7)then the car was driven 49335 miles, if x≡4 (mod 7)then the car was driven 149335 miles, and if x≡2 (mod 7)then the car was driven 249335 miles