MeMe22 one year ago An electronics company has developed a new hand-held device. The company predicts that the start-up cost to manufacture the new product will be \$225,000, and the cost to make one device will be \$7.50. If the company plans on selling the devices at a price of \$9, write and solve an inequality to determine how many must be sold for the company to make a profit. Show your work.

1. DemolisionWolf

So we'll do this in pieces. what is the cost of the company? cost of company to start = ?

2. MeMe22

225,000

3. DemolisionWolf

yes, so profit = -22500 now if we we want to make any money, profit, we need to sell devices, what would the eqwuation look like if I wanted to know how much money I make for each device I sell?

4. MeMe22

umm im not sure

5. DemolisionWolf

it would look like this: how much money is made when each device is sold=9*x where x is the number of devices sold

6. DemolisionWolf

I have to go soon..

7. MeMe22

ok

8. DemolisionWolf

so now our equation would look like this: profit = 9*x -22500 can you do what I did with the 9x but with how much it costs to make each device?

9. MeMe22

yes 7.50*x-22500 right?

10. DemolisionWolf

very good, but I was a bit confusing when I asked you to do it ^_^ so now if we combine all the parts, the -22500 and 9*x and -7.50*x we get profit = 9x-7.5x-2500

11. MeMe22

ok

12. DemolisionWolf

profit = 9x-7.5x-22500 now we need to set the equation equal to x so we move the 22500 to the other side: 22500 = 9x-7.5x now we factor out the x on the right side 22500 = x(9-7.5) simpilfy 22500 = x(1.5) divide both sides by 1.5 22500/1.5 = x now change the = sign to an inequality 22500/1.5 < x so in order for a company to make any profit, x must be greater than 22500/1.5 so, I sorta rushed it all at the end, but I have to go ^_^

13. MeMe22

alright, thank you for the help!!

14. DemolisionWolf

^_^ we did the hard part of setting up the equation. and all the stuff I rushed was just algebra stuff