SOLUTION: Solving Problems with Quadratic Equations
17. Sherri sells photos of athletes to baseball, basketball, and hockey fans after their games. Her regular price is $10 per photograph,
Question 198591: Solving Problems with Quadratic Equations
17. Sherri sells photos of athletes to baseball, basketball, and hockey fans after their games. Her regular price is $10 per photograph, and she usually sells about 30 photographs. Sherri finds that, for each reduction in price of $0.50, she can sell an additional two photographs.
a) Total sales revenue is the product of the number of units sold and the price. Make an algebraic model to represent Sherri's total sales revenue.
b) At what price will Sherri's revenue be $150?
c) At what price will her maximum revenue occur?
d) At what price will her revenue be $0?
e) Graph the relationship between revenue and the number of price reductions. Which features on the graph represent the solutions to parts b), c), and d)?
Thanksssssss Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! regular price is $10 per photograph, and she usually sells about 30 photographs.
Sherri finds that, for each reduction in price of $0.50, she can sell an additional two photographs.
:
Let x = ea 50 cent reduction & also = ea photograph increase
:
a) Total sales revenue is the product of the number of units sold and the price. Make an algebraic model to represent Sherri's total sales revenue.
Revenue = price * pictures sold
Rev = (10-.5x)*(30+2x)
FOIL
f(x) = 300 + 20x - 15x - x^2
f(x) = -x^2 + 5x + 300
:
;
b) At what price will Sherri's revenue be $150?
-x^2 + 5x + 300 = 150
-x^2 + 5x + 300 - 150 = 0
-x^2 + 5x + 150 = 0
Multiply equation by -1 (easier to factor)
x^2 - 5x - 150 = 0
Factors to:
(x-15)(x+10) = 0
Positive solution;
x = 15
Price: 10 - .5(15) = $2.50 for $150 revenue
;
Revenue Check: 2.50(30+2(15)) = $150
:
:
c) At what price will her maximum revenue occur?
Find the axis of symmetry of the equation: y = -x^2 + 5x + 300
x =
x =
x = 2.5
price(10-.5(2.5)) = 8.75
:
:
d) At what price will her revenue be $0?
-x^2 + 5x + 300 = 0
x^2 - 5x - 300 = 0
(x-20)(x+15) = 0
x = 20
Price: 10 - .5(20) = $0
;
:
e) Graph the relationship between revenue and the number of price reductions. Which features on the graph represent the solutions to parts b), c), and d)?
b: x=15 price reductions; about $150
c: you can see max rev occurs when x = 2.5
d: x=20, rev = 0
