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Lets say for whatever reason You can't do a pushup to save your life.
You can't manage the technique and it hurts you too much.
Or lets say you're like me and can't do a sit up to save your life because your legs end up pulling you up rather than your core muscles.
Now lets assume you're in average shape (Not too lean, not too round) and for easy calculations sake that your body in total weighs 100 kilo.
(The reason for 100 is that everyone can easily work out a percentage and apply it to their own weight once the answers flood in)

With those parameters in mind, which piece of equipment(s) at a Gym and with how much weight would equate to a push up, a sit up and a pull up?

The reasons for this question is like I say, I struggle with sit ups. I'm getting better at pushups and I'm just able to endure three pull-ups without crying afterwords.
But situps are something I just can't do. However, there is a machine at my gym that I think will equate to a sit up if I apply enough weight to it.
Rather than asking for myself I figured I may as well generalise the question so more readers can benefit form the answers.

Trying to calculate in advance how much weight an untrained individual should be able to use in their first session is an exercise in futility.

First session in the gym, just start with a weight that would be trivially easy to lift for your target number of repetitions. That's your first warm-up set. Then increase the weight set by set until it gets to the point where completing your target number of repetitions is actually hard work. Congratulations, you've just found your working set weight.

For subsequent sessions, you don't need to do so many sets to find your working weight. Just make a small increment to either the weight or number of repetitions you're aiming for, and then do 2-3 sets working up to that. E.g. Say last session you managed 10 reps on lat pulldown at 49kg, and the machine has 7kg increments, then you might try for 12 reps at 49kg this time. So you might warm up with a set of 12 at 21kg, another set at 35kg, and then you're ready for your work sets at 49kg.

Also, it is impossible for your legs to pull you up rather than your core in a situp. If your shoulders come off the ground, your abs are active in holding your spine up. Without them, your spine would arch back and all your leg muscles (hip flexors, specifically) could do is pull your lower back up into an arch with shoulders dragging on the ground.