Assistance in understanding and solving this example on Elementary Number Theory with the details of the solution to better understand, thanks.a) Find all solutions to 3x+4y=60 in positive integers.b) A roadside stand bought 11 large baskets of eggs from a farmer and sold 39 small baskets of eggs, which hold fewer than a dozen. There were 19 eggs left over. How many eggs does a large basket hold?

Answer:a) x  |  y==========16  |  312  |  68   |  94   |  12b) A large basket contains 23 eggsStep-by-step explanation:a) Isolating 3x, we get3x = 60-4yThis means that 60-4y is a multiple of 3.Besides, as x is a positive integer, then x = 60-4y has to be greater than zero60-4y>0Solving the inequality for y60>4y60/4 > y15>y (or y<15, which is the same)The multiples of 3 which are smaller than 15 are 3,6,9 and 12Now we draw a table for these values of y and found the value of x by replacing in the equation 3x = 60-4y---> x = (60-4y)/3 x  |  y=======16  |  312  |  68   |  94   |  12And these are all the solutions in positive integers.b) This problem is pretty much like problem a)Let's call x the number of eggs contained in the large baskets and y the number of eggs contained in the small baskets.ThenNumber of eggs bought - number of eggs sold = number of eggs left over.In this case11x-39y = 19But we also know that 0<y<12 because the small baskets hols fewer than a dozen.Isolating x in the equation 11x-39y + 19, we getx=(19+39y)/11Now we make a table with these values of x and y remembering that y is a positive integer smaller than 12x   | y=======5.2  | 18.8  | 212.4 | 315.9 | 419.5 | 523   | 626.6 | 730.1 | 833.6 | 937.2 |1040.7 |11From this table we see that the only integer solution for x is 23, so a large basket contains 23 eggs.