Find the largest integer less than 74 that leaves a remainder of 3 when divided by 7.
I need to find an integer that is of the form 7k + 3, where k is a whole number, and that is less than 74. I can start by trying the largest possible value of k, which is 10, since 7(10) + 3 = 73, which is still less than 74. If I try k = 11, then 7(11) + 3 = 80, which is too big. So, k = 10 is the largest value of k that works, and the corresponding integer is 7(10) + 3 = 73. Therefore, the largest integer less than 74 that leaves a remainder of 3 when divided by 7 is 73.

