When bicycles are sold for $300 each, a cycle store can sell 70 in a season. For every $25 increase in the price, the number sold drops by 10.

Represent the sales revenue as a function of the price.

The total sales revenue is $17,500. How many bicycles were sold? What is the price of one bicycle?

What range of prices will give us sales revenue that exceeds $18,000?

Micheala95
May 13, 2017

#1**+1 **

When bicycles are sold for $300 each, a cycle store can sell 70 in a season. For every $25 increase in the price, the number sold drops by 10.

Represent the sales revenue as a function of the price.

The total sales revenue is $17,500. How many bicycles were sold? What is the price of one bicycle?

What range of prices will give us sales revenue that exceeds $18,000?

The sales revenue (per bike) can be represented by ( 300 + 25x) where x represents the number of $25 increases

The revenue function, R(x) can be represented as

R(x) = ( 300 + 25x) ( 70 - 10x) = -250x^2 -1250x + 21000

For $17500, we have

17500 = -250x^2 - 1250x + 21000

250x^2 + 1250x - 3500 = 0 divide through by 10

25x^2 + 125x - 350 = 0 divide through by 25

x^2 + 5x - 14 = 0 factor

(x + 7) ( x - 2) = 0

Set each factor to 0 and solve for x .... when x = 2 ..... the price of one bike = (300 + 2(25)) = $350 and the number of bikes sold = (70 - 10(2) ) = 50

And when x = - 7 the price of a bike = (300 + 25(-7) ) = $125 and the number of bikes sold = (70 - 10(-7) ) = 140

To find the range of prices where sales revenue > $18000 look at the graph here :

https://www.desmos.com/calculator/gindgnqtxq

The graph shows that the revenue will > $18000 when x ≈ about -6 to x ≈ 1

In other words, when the price of a bike is from ≈ (300 + 25(-6) ) ≈ $ 150 to ≈ (300 + 25 (1) ) ≈ $325

CPhill
May 14, 2017