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.
