Question

A bicyele store costs $2400 per month to operate. The store pays an average of $60 per bike. The average selling price of each bicyeIs $120How many bicycles must the store sell each month 1o break even?Write a system of equations to represent the situation, then solve*Show both the equations and the solution

Answer 1

The system of equations is:

• C(x)=2400+60x

,

• R(x)=120x

The number of bicycles to break even = 40

Explanation:

Let the number of bikes sold = x

• The operating cost of the store per month = $2400

,

• Cost Price Per bike = $60

Thus, the total monthly cost for the store:

`C(x)=2400+60x`

Next, the average selling price of each bicycle is $120, therefore, the monthly revenue of the store:

`R(x)=120x`

The store breaks even when the cost equals its revenue.

`\begin{gathered} R(x)=C(x) \\ 120x=2400+60x \end{gathered}`

We then solve for x:

`\begin{gathered} \text{ Subtract 60x from both sides of the equation} \\ 120x-60x=60x-60x+2400 \\ 60x=2400 \\ \text{ Divide both sides of the equation by 60} \\ (60x)/(60)=(2400)/(60) \\ x=40 \end{gathered}`

The store must sell 40 bicycles in order to break even.