Jada has a stand in the marketplace where she sells ground cumin. Her weekly expenses are $300.

Question

She sells her cumin at a fixed price per kilogram. If she sells 120 kilograms of cumin, her weekly net profit is $600. 

 

1. What is the price of a kilogram of Jada's cumin?

 

2. How much cumin does Jada have to sell to cover her weekly expenses?

Answer 1

This can be solved mathematically. Net profit is the profit after expenses have been removed, so for that week her total profit would be $900

 

$600+$300=$900

 

So if she sold 120 kg that week and made $900 we can just divide what she sold into what she made to discover the cost of each kg.

 

$900/120kg=7.50$/kg

 

Therefore the price of one kg is $7.50

 

If you know what one kg costs you can calculate how much she needs to sell to make her expenses of $300 by dividing how many times $7.50 goes into $300

 

$300/$7.50=40

 

To check the answer think of it backwards. So if someone buys 40kg of cumin at $7.50 she would make $300 and expenses are covered. If she sold 120kg at $7.50 she would make $900 and then subtract her weekly expenses and she has a net profit of $600

Answer 2

Think of Jada's weekly expenses as a constant subtraction from her net profit. Then we can define the variables.

 

Let y = Jada's weekly net profit.

Let x = how many kilograms of cumin Jada sells

Let p = price per kilogram of cumin

 

Net profit is money earned minus expenses, so --> y = px-300

 

We know that when x=120, y=600. We can use this to solve for p.

 

600=p(120)-300

900=120p

900/120=p

7.5=p

-->Her cumin costs $7.50 per kilogram.

 

To cover her weekly expenses, her minimum net profit must be zero (and not negative).

 

0=7.5x-300

300=7.5x

300/7.5=x

40=x

-->Jada must sell 40 kilograms of cumin to cover her weekly expenses.