Bugs in the Garden

In Sam and Jill's garden there are two sorts of ladybirds. There are red Seven-Spot ladybirds with $7$ black spots and shiny black Four-Spot ladybirds with $4$ red spots.

Sam and Jill looked at a leaf with three ladybirds on it.

"One Seven-Spot ladybird," said Sam, "and two Four-Spot ones."
"That's $15$ spots altogether!" laughed Jill.
"I wonder if we could find ladybirds whose spots add to other numbers. I know how to do $16$."
"And $14$ is easy too," added Sam.

How would you make $16$ and $14$ spots with the Seven-Spot and Four-Spot ladybirds?

What other numbers can you make with adding $4$s and $7$s?
Can you get lots of numbers from say $4$ to $35$?
Are there some numbers you can't get?