Question 974869
x = 1 mod 3
x = 2 mod 5


First find the integers that satisfy the first two conditions. The first number that works is 7, the next is 22, and so on. Any number of the form 7 + 15n, where n is a positive integer, leaves a remainder of 1 when divided by 3 and a remainder of 2 when divided by 5.


7 + 15n > 100
15n > 93
n > 6.2 ----> n = 7


We will start looking from 7 + 15(7) = 112 and beyond. 112 is divisible by 7 and 15 leaves a remainder of 1 when divided by 7, so the number that satisfies all three conditions is:


112 + 15(3) = 157.