### Instruction: Find the largest integer less than 80 that leaves a remainder of 3 when divided by 5.### Response: To find the largest integer less than 80 that leaves a remainder of 3 when divided by 5, I need to think about what it means to leave a remainder of 3 when divided by 5.
That means that the integer is 3 more than a multiple of 5, or it has the form 5k + 3, where k is some integer.
So I want to find the largest value of k such that 5k + 3 is less than 80.
I can start by trying some values of k, like k = 15, 16, 17, and see when 5k + 3 becomes too big.
If k = 15, then 5k + 3 = 78, which is less than 80 and a possible candidate.
If k = 16, then 5k + 3 = 83, which is too big.
If k = 17, then 5k + 3 = 88, which is also too big.
So it seems that k = 15 is the largest value of k that works.
Therefore, the largest integer less than 80 that leaves a remainder of 3 when divided by 5 is 5k + 3 = 78.