La spent her whole allowance of $2.00, plus the 16¢ she had left over from last week, onbubble gum. if the pieces of gum had been a penny cheaper, she would have received threemore pieces than she did. how many pieces did she actually buy?

Let the number of pieces of gum be g and the cost of each piece be c.
gc=2.16. Also, (g+3)(c-0.01)=2.16.
So gc=(g+3)(c-0.01)=gc-0.01g+3c-0.03.
And -0.01g+3c=0.03 and c=2.16/g. -0.01g+6.48/g=0.03.
-0.01g²+6.48=0.03g; 0.01g²+0.03g-6.48=0 which can be more conveniently written:
g²+3g-648=0=(g+27)(g-24) so g=24, the number of pieces she actually had.
CHECK The cost of the gum, c=2.16/24=9 cents.
A penny cheaper makes the gum 8 cents a piece and she could have bought 27 pieces instead of 24.