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Cherries Come in Twos

Age 7 to 11 Challenge Level:

Susie had a large bowl of cherries.

Bowl of Cherries

They were all in pairs.

4 pairs of cherries

Susie took out a pair, she ate one cherry and put the other one back. She took out another pair and did the same again.
Then she helped herself to one of the single cherries in the bowl.

Susie continued helping herself to the cherries in this way (pair, pair, single - pair, pair, single - ...)

two pairs and one cherry

After she had done this lots of times, there were just $14$ single cherries left.

How many cherries had there been in the bowl to start with?