Please solve this with explanation

1. Find all simultaneous solutions to the following systems of linear congru- ences: (a) T = 15 mod 27 T = 16 mod 20 2x - 5=5 mod 12 (b) 7x - 2 =1 mod 10 4x + 3 = 11 mod 15 2. The three children in a family have feet that are 5 inches, 7 inches, and 9 inches long. When they measure the length of the dining room of their house using their feet, they each find that there are 3 inches left over. How long is the dining room