Final answer:
Jane originally had 11 pieces of candy in her bag. To find this, an equation was set up and solved based on the information that she received 5 more pieces than her original amount and then had 27 pieces in total.
Step-by-step explanation:
To find out how many pieces were in Jane's original bag of candy, we need to work backwards from the information provided. We know that after giving some pieces away and then receiving 5 more than she had originally, Jane has 27 pieces. Let's define the number of candies Jane originally had as x. After giving some away, she still had x candies. Then her grandmother gives her x + 5 candies, and we know that results in Jane having 27 pieces in total.
Therefore, the equation to solve is:
x + (x + 5) = 27
Combining like terms, we get:
2x + 5 = 27
Subtracting 5 from both sides gives us:
2x = 22
Dividing both sides by 2 gives us:
x = 11
So, the original number of candy pieces Jane had is 11.