I split my push-ups usually between 50 normal ones and 50 "wide" ones to get the pecs. Do I do them correctly? Hah. Probably not half of them. I try to keep myself planked, but of course my stomach slips toward the floor sometimes. Generally just make sure you're actually using those muscles. Forget about a coach. You know if you're doing it or "cheating".

Instead of 50/wk. Try 10/day. Just from my own experience, there's a benefit to a short concentrated burst of activity on a daily basis, versus a longer one on a weekly basis.