SOLUTION: When a vendor prices key chains at $5 each, she sells 210 key chains. For each $1 she raises the price, she sells 10 fewer key chains. USE AN EQUATION to determine what she should

Question 813641: When a vendor prices key chains at $5 each, she sells 210 key chains. For each $1 she raises the price, she sells 10 fewer key chains. USE AN EQUATION to determine what she should charge to maximize her revenue from sales.
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
use the revenue equation:
r = p * n
where
p = price per item
n = number of items sold
---
because we know that changing the price (p) also changes the number sold (n), we need to introduce a variable to the revenue equation to measure the changes in p and n.
---
so just make up a variable, call it x, such that:
p + x means a one dollar price increase and
p - x means a one dollar price decrease and
n + x means a one item number-sold increase and
n - x means a one item number-sold decrease
---
for each $1 price increase (p + x) there are 10 fewer items sold (n - 10x), so:
---
r = (p + x) * (n - 10x)
---
we know that at $5 per item, she sells 210 items, so:
r = (5 + x) * (210 - 10x)
---
r = (5 + x) * (210 - 10x)
r = 1050 - 50x + 210x - 10xx
r = -10xx + 160x + 1050
---
the above quadratic equation is in standard form, with a=-10, b=160, and c=1050
---
to solve the quadratic equation, plug this:
-10 160 1050
into this: https://sooeet.com/math/quadratic-equation-solver.php
---
Answer 1:
the quadratic equation has a maximum at: ( x=8, r=1690 ), so:
maximum revenue is $1690
when price per item is $8
---
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
---
Convert fractions, decimals, and percents:
https://sooeet.com/math/fraction-decimal-percent.php
---
Calculate and graph the linear regression of any data set:
https://sooeet.com/math/linear-regression.php
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