50 pushups, even 7 pushups, with proper technique can be very hard - not cheating push-ups. Proper, all the way to the ground, and hands appropriately spaced.
Try this:
Do one push-up in any position.
Now do another, but with your hands each about 8-10 inches further outwards from last time.
Now do another, but with your hands each about 8-10 inches inwards from the first time.
Now use the first position again but move them 8 inches back.
Now again, 8-10 inches forward from the first position.
See how much difference there is?
History tells me it takes me about 8 weeks to work back up to being able to do 100.
For those doing core training, we should really also be counting V-Snaps and Bridge twists.