Cassy had a bag of candy and was heading to the playground when she was
intercepted by her arch nemesis, Rachelle. Rachelle thought Cassy had made fun
of her the pervious day, so Rachelle tried to grab the bag of candy away from
Cassy. In the ensuing battle, half the candy plus two pieces fell on the ground.

Let's be careful here to interpret this as two separate steps:

1. First, half the pieces fell on the ground. 
2. Then second, 2 pieces fell on the ground. 
  
Cassy maintained control of the bag and ran to the office to tattle on
Rachelle. On the way to the office Cassy ran into Julio, whom she had a crush
on. She gave Julio some of the candy in her bag, which just happened to be
equal to one-fourth of what was left, plus five pieces. 

Let's again be careful here to interpret that as two steps:

1. First, she gave Julio 1/4 of the pieces. 
2. Then second, she gave him 5 more pieces. 

Just before Cassy got to the office her best friend Madison caught up with her.
Cassy gave Madison half of the candy she had left. When Cassy got to the office
and told the story to the principal, he asked to see the bag of candy. He told
Cassy he would talk to Rachelle, but that it was against school policy to have
candy on the campus. He then ate the remaining two pieces of candy. How many
pieces of candy were originally in the bag?

Show the movie backwards. The principal takes two pieces of candy out of his
mouth [gross! :) ] and puts them in the bag and gives it to Cassy. 

Cassy then takes her bag containing the 2 pieces and walks backward out of the
principal's office. 

Then Madison gives Cassy enough to double the 2 she has in her bag, that is,
Madison gives Cassy another 2 pieces and Cassy puts them in her bag, so now
there are 4 pieces in her bag. 

Then she walks backward away from Madison and then meets Julio.
Julio first gives Cassy 5 more pieces, which she put in her bag. So now Cassy
has 9 pieces in her bag. 

Now, remembering the two steps, Julio then gives her some more pieces to put in
her bag.  Before Julio gives her these extra pieces, she has only 3/4 as many
as she will have after he gives them to her.  She now has 9, which is three
groups of 3, so each of those 3 groups of 3 is a fourth of what will have after
Julio gives her the other fourth.  So the other fourth he must give her must
must be the same as each of the three fourths she has in her bag. So he gives
her the other fourth, which must therefore also be 3 pieces.  Now Cassy has 12
pieces in her bag.

Now she walks backwards and meets up with her rival Rachelle. Then 
(remembering the two steps)

1. 2 pieces of candy magically jump up off the ground and into her bag.

She had 12 before meeting Rachelle, and so now she has 14 pieces of candy.
Then,

2. Enough candy jumps up off the ground and into the bag to double the number
of pieces in the bag.  

Since she had 14 pieces before the second batch of candies jumped up off the
ground into her bag, 14 more had to jump up off the ground into her bag.  So
how her bag contains 28 pieces of candy.  Now we come to the end of the
backwards movie of what happened.  

So the answer is:  Cassy had 28 pieces of candy in her bag.

-------------------

Now let's check it (forward) to see if 28 is correct:

Cassy had a bag of 28 pieces of candy and was heading to the playground when
she was intercepted by her arch nemesis, Rachelle. Rachelle thought Cassy had
made fun of her the pervious day, so Rachelle tried to grab the bag of candy
away from Cassy. In the ensuing battle, half the candy, 14 pieces, plus two
pieces fell on the ground, making a total of 16 pieces falling to the ground.
That left Cassy with 28-16 or 12 pieces in her bag.  Cassy maintained control
of the bag and ran to the office to tattle on Rachelle. On the way to the
office Cassy ran into Julio, whom she had a crush on. She gave Julio some of
the candy in her bag, which just happened to be equal to one-fourth of what was
left, which was 3 pieces, plus five pieces. So she gave Julio 8 pieces, leaving
her with just 4 pieces in her bag. Just before Cassy got to the office her best
friend Madison caught up with her. Cassy gave Madison half of the candy she had
left, which was 2 of the 4 pieces.  So she only had 2 pieces left.  When Cassy
got to the office and told the story to the principal, he asked to see the bag
of candy. He told Cassy he would talk to Rachelle, but that it was against
school policy to have candy on the campus. He then ate the remaining two pieces
of candy. 

So it checks.  28 pieces is the correct answer.

-------------------------

Now since you are taking algebra, your teacher may not accept the backwards
movie method, and wants you to use algebra.  If this is the case, then we'll
just "check" it as above but this time use N pieces of candy instead of 28.

Cassy had a bag of N pieces of candy and was heading to the playground when she
was intercepted by her arch nemesis, Rachelle. Rachelle thought Cassy had made
fun of her the previous day, so Rachelle tried to grab the bag of candy away
from Cassy. In the ensuing battle, half the candy, N/2 pieces, plus two pieces
fell on the ground, making a total of N/2 + 2 pieces falling to the ground.
That left Cassy with N - (N/2 + 2) pieces in her bag.  Cassy maintained control
of the bag and ran to the office to tattle on Rachelle. On the way to the
office Cassy ran into Julio, whom she had a crush on. She gave Julio some of
the candy in her bag, which just happened to be equal to one-fourth of what was
left, which was [N - (N/2 + 2)]/4 pieces, plus five pieces. So she gave Julio
[N - (N/2 + 2)]/4 + 5 pieces, leaving her with just 

N - (N/2 + 2) - {[N - (N/2 + 2)]/4 + 5}

pieces in her bag. Just before Cassy got to the office her best friend Madison
caught up with her. Cassy gave Madison half of the candy she had left, which
was [N - (N/2 + 2) - {[N - (N/2 + 2)]/4 + 5}]/2 

of the 

N - (N/2 + 2) - {[N - (N/2 + 2)]/4 + 5} pieces.  So she only had

[N - (N/2 + 2) - {[N - (N/2 + 2)]/4 + 5}]/2 

pieces left.  When Cassy got to the office and told the story to the principal,
he asked to see the bag of candy. He told Cassy he would talk to Rachelle, but
that it was against school policy to have candy on the campus. He then ate the
remaining two pieces of candy. 

Therefore we now have the equation, 

[N - (N/2 + 2) - {[N - (N/2 + 2)]/4 + 5}]/2 = 2

Multiply both sides by 2

N - (N/2 + 2) - {[N - (N/2 + 2)]/4 + 5} = 4

Remove the first parentheses:

N - N/2 - 2 - {[N - (N/2 + 2)]/4 + 5} = 4

Remove the braces {}:

N - N/2 - 2 - [N - (N/2 + 2)]/4 - 5 = 4

Multiply through by 4

4N - 2N - 8 - [N - (N/2 + 2)] - 20 = 16

Remove the parentheses inside the brackets:

4N - 2N - 8 - [N - N/2 - 2] - 20 = 16

Remove the brackets:

4N - 2N - 8 - N + N/2 + 2 - 20 = 16

Multiply through by 2

8N - 4N - 16 - 2N + N + 4 - 40 = 32

Combine terms on the left:

3N - 52 = 32

Add 52 to both sides

     3N = 84

Divide both sides by 3

     N = 28

Edwin