Break even question/problem?

Formula for profit/loss on the books is:

SP = selling price, PP = purchase price, R = rent, x = number of books sold

(SP - PP) x - R

(Notice Rent is not dependent on number of books sold)

(80 - 50) x - 3000 => 30x - 3000

where x is the number of books sold.

(1) Breakeven pt means not profit or loss, so set equation equal to 0

30x - 3000 = 0

30x = 3000

x = 100

(2) 100 books sold * $80 (selling price) = $8,000

(3) 30 (60) - 3000 = $1,200 LOSS

(4) 30 (150) - 3000 = $1,500 PROFIT

(5) Set equation equal to 3000

30x - 3000 = 3000

30x = 6000

x = 200 books

(6) PP = $80 * 1.25 = $100

(100-50) x - 3000 = 0

50x - 3000 = 0

50x = 3000

x = 60 books

Let

n = number of books

Cost = Rent + Cost of Books = 3000 + 50n

Revenue = 80n

<< How many books would the students have to sell to breakeven? >>

To break even, Revenue = Cost, hence

80n = 3000 + 50n

Solving for "n",

n = 3000/30 = 100 books

<< What would be the breakeven sales volume in dollars? >>

Breakeven sales in dollars = 80(100) = $8,000.

<< How much profit or loss would the business have if it sold 60 books? >>

Profit/(Loss) = Revenue - Cost

and for n = 60,

Profit/(Loss) = 80(60) - 3000 - 50(60)

Profit/(Loss) = $(1200) ---- loss

<< How much profit or loss would the business have if it sold 150 books? >>

For n = 150,

Profit/(Loss) = 80(150) - 3000 - 50(150)

Profit/(Loss) = $1500 --- profit

<< How many books would the students have to sell to make a target profit of 3,000? >>

Profit/(Loss) = Revenue - Cost

3000 = 80n - 3000 - 50n

3000 + 3000 = 30n

30n = 6000

n = 200 books

<< The students were able to convince customers that the books have more value and were able to increase the selling price of a book by 25 percent, what would be the new number of books the company must sell to breakeven? >>

New selling price = 80*(1.25) = 100, hence the new equation for

Revenue = 100n

Since Cost will remain the same, then

100n = 3000 + 50n

and solving for "n",

100n - 50n = 3000

50n = 3000

n = 60 books