Your jewelry business orders $1320 in supplies each month. In each month, you can usually sell an earring/ring set for about $55 each. How many sets do you need to sell each month to break even?

If you found that your total profit for a month was $715, how many sets did you sell?

If you had a month where 7 sets were sold, how much profit did you make?

Given,

The jewelry business orders $ 1320 in supplies each month.

That is, the invested amount = $ 1320,

Also, the selling price of each earring/ring set = $ 55,

Part 1 : Let x be the number of set that have been sold each month to break even (in which revenue and invested amount are equal)

So, Total revenue (the cost of x sets) = 55x,

⇒ 55x = 1320

Divide both sides by 55,

We get,

x = 24

Hence, 24 sets are needed to sell each month to break even.

Part 2 : Let y be the number of sets in which the profit is $ 715,

Total revenue = 55x

Profit = Total revenue - invested amount

⇒ 55x - 1320 = 715,

⇒ 55x = 715 + 1320

⇒ 55x = 2035

⇒ x = 37

Hence, 37 sets are sold for the total profit of $715.

Part 3:

Revenue in selling 7 sets = 55 * 7 = $ 385

Profit = $ 385 - $ 1320 = - $ 935

Hence, the profit is - $ 935 after selling 7 sets.