Hi,

Let n represent the number of bikes needed to be sold to break even

Write as You Read:

$3600 + $55n = $95n

$3600 = $40n

n = 90    the number of bikes needed to be sold to break even

Wish You the Best in your Studies. 

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
 they have a fixed cost per month of 3600.

this cost remains no matter how many bikes they sell.

they pay an average of 55 per bike.

they sell each bike for an average of 95.

their profit is 95 - 55 = an average of 40 per bike.

3600 / 40 = an average of 90 bikes that have to be sold per month to break even.

the algebraic formula for the cost is:

c = 3600 + 55 * x

x represents the number of bikes bought and sold.

the algebraic formula for the revenue is:

r = 95 * x

the algebraic formula for the profit is:

p = r - c

this becomes:

p = 95 * x - (3600 + 55 * x)

simplify this formula to get:

p = 95 * x - 3600 - 55 * x

simplify to get:

p = 40 * x - 3600

you break even when the profit is equal to 0.

the formula becomes:

0 = 40 * x - 3600

add 3600 to both sides of this equation to get:

3600 = 40 * x

solve for x to get:

x = 90.

when 90 bikes are bought and sold, .....

the cost is 3600 + 55 * 90 = 8550 and the revenue is 95 * 90 = 8550.

the profit is revenue minus cost = 0.

that's the break even point.

you can graph the revenue and the cost equations and you will see that the break even point is when the number of bikes bought and sold is 90.









 

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