Word problem help :(

Question

suppose you are setting up a small business and have invested $5,000 to produce an item that sell for $9. if each unit can be produced for $7, how many units must you sell to break even?

Answer 1

Hi Saadia:

 

You can think of it this way:

 

You're making 2 dollars at a time. In order to make 5,000 dollars, you need to make 2 dollars 2,500 times.

 

Cheers,

 

Matt in NY

Answer 2

To get started you need to set up two equations, one for profit and one for cost. 

 

Let p = profit and c = cost and x=number of units

 

so we have to define Y(p) and Y(c)

 

Profit: the profit is $9 per unit so we set up our equation like this 

 

Y(p) = 9x

 

Cost: we have the one time investment of $5000 and its cost $7 per unit to make them. So we set up the equation like this

 

Y(c) = 5000 + 7x

 

now we need to find when we start making more profit than the cost. to do so put the lines On a graph. The point where they intersect will be where the profit is greater than the cost. I would suggest you graph them either on paper or a graphing calculator just so you can visually confirm that is true. 

 

To find out how many units need to be sold in order to break even we need the intersection of the two lines. 

 

To to find the intersection of two lines you set them equal to each other and solve for x.

 

Y(p) = Y(c)

 

9x = 5000 + 7x

 

Now solve for x.

 

9x = 5000 + 7x

 

2x = 5000

 

x = 2500

 

Now just put it into words. You need to sell 2500 units in order to break even.