SOLUTION: Ella spent her whole allowance of $2.00, plus the 16� she had left over from last week, on bubble gum. If the pieces of gum had been a penny cheaper, she would have received three

Question 823924: Ella spent her whole allowance of $2.00, plus the 16� she had left over from last week, on 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?
Found 2 solutions by richwmiller, TimothyLamb:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
216=cg,
216=(c-1)*(g+3)
c=9 g=24

Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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x = price per gum
y = number of pieces
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xy = 216
y = 216/x
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(x - 1)(y + 3) = 216
xy + 3x - 1y - 3 = 216
---
x216/x + 3x - 1(216/x) - 3 = 216
216 + 3x - 216/x - 3 = 216
3x - 216/x = 3
3xx - 216 = 3x
3xx - 3x - 216 = 0
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the above quadratic equation is in standard form, with a=3, b=-3, and c=-216
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
3 -3 -216
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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this quadratic has two real roots (the x-intercepts), which are:
x = 9
x = -8
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negative price doesn't make sense, so use the positive root
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answer:
x = price per gum = $0.09
y = number of pieces = 24
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
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