Question

Adah produces scented candles. The cost of producing a candle is $1.25. Adah sells a candle for $2.50. She has a start-up costs of $300.

a) Write a system of two equations that models this situtaiton.

b) Determine the number of candles Adah must sell to break even. Solve the system using your chosen method and identify the method used.

Answer 1

Answer:

(a) The system of two equations are

c = $300...(1)

p = x × ($2.50 - $1.25)...(2)

(b) The number of candles she must sell to break even are 240 candles

Step-by-step explanation:

The cost of of producing a candle = $1.25

The price at which Adah sells a candle = $2.50

The stat-up cost of producing candles = $300

(a) Let c represents the start-up cost of producing candles, let p represent the profit Adah makes from selling candles and x represents the number of candles sold, we have;

c = $300...(1)

p = x × ($2.50 - $1.25)...(2)

(b) The number of candles Adah must sell to break even is given as follows;

At break even point, Start-up cost = Profit

∴ c = p

300 = x × (2.50 - 1.25) = 1.25·x

∴ x = 300/1.25 = 240

Therefore;

The number of candles she must sell to break even = 240 candles