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Here's a third variation on ketchup.
Take tomato paste, add sugar to taste. Add onion and garlic powder.  Add some mustard, perhaps spicy brown or even yellow is best.
Add French's or Heinz Worcestershire sauce to taste and to thin the tomato paste somewhat.
This is quick and dirty, but good if done right.

it is also a good ingredient for thousand lsland, or Russian, dressing, preferably using home made mayonnaise as a base.