Question

Ella spent her whole allowance of $2.00, plus the 16¢ she had left over from last week, in bubble gum. If the pieces of gum had been a penny cheaper, she would have received three more pieces than she did. How many pieces did she actually buy?
(A) 8
(B) 9
(C) 16
(D) 24
(E) 27

Answer 1

Let x be the number of pieces that Ella bought.
So, the cost of one piece is 2.16/x
A penny chipper means (2.16/x-0.01) per piece. 
And  (2.16/x-0.01)*(x+3)=2.16

Now, we will try to solve the following equation:
$(\frac{2.16}{x}-0.01)\times(x+3)=2.16.$

Solving the above equation for x we get x=24. Answer D.

Answer 2

The answer here is simple to work out. We know that Ella has a total of $2.16. We need to determine each piece of gums value.   
We also know that if the pieces of gum were one penny cheaper, she would have received three additional pieces.  
 At 8 pieces we know that each piece costs 27 cents. If the pieces of gum were one cent cheaper, she would have ended up with 8.64 pieces. Even with rounding, because the answer is not 11, we know that this is incorrect.  
 At 9 pieces we know that each piece costs 24 cents. If the pieces of gum were one cent cheaper, she would have ended up with 9.39 pieces. Even with rounding, because the answer is not 12, we know that this is incorrect.  
 At 16 pieces we know that each piece costs 13.5 cents. If the pieces of gum were one cent cheaper, she would have ended up with 17.28 pieces. Even with rounding, because the answer is not 19, we know that this is incorrect.  
 At 24 pieces we know that each piece costs 9 cents. If the pieces of gum were one cent cheaper, she would have ended up with 27 pieces. We know this is the correct answer because 27-24 is 3. 
 The correct answer is D) 24