Question

Ella 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?

Answer 1

If x is the first price of bubble gum and
y is the number of prices she bought

$2.00+16 cents= 216 cents
216/x=y

If the first price will be 1 penny cheaper the price will be (x-1) and will get 3 more pieces of candy so will have y+3

216/(x-1)=y+3

Since both 216/x=y and 216/(x-1)=y+3 can be true in the same time this is a system of equations that will help us find y.

If 216/x=y then x=216/y
Substitute x in the other equation
216/(216/y)-1=y+3
y^2 +3y-648=0
And y could be 24 pieces and 27 pieces

Check
216cents /24 pieces= 9 cents per piece
Cheaper by 1 penny will be 8 cents
216//8=27 pieces that are 3 more than 24

Same logic for 27 pieces bought