Ladybirds in the garden

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

Problem

Ladybirds in the Garden printable sheet

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

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

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"One Seven-Spot ladybird," said Sam, "and two Four-Spot ones."

"That's 15 spots altogether!" said 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 4s and 7s?

Can you get lots of numbers from 4 to 35?

Are there some numbers you can't get?