1. ## [SOLVED] Difficult Problem..

Hi i have a "challenge" problem that i have to solve. I have no idea how i should write the equation to solve this. I don't understand how I can make an equation to answer both parts of the question. Should i use 2 variables? One for price and one for the number of magnets produced? Please take a look.

The question is: your company makes fridge magnets. The materials for each magnet is $0.14. Your company has additional expenses of$27 000 year. The per-magnet cost is $\displaystyle \frac{total-costs-per-year}{number-produced-per -year}$. If your company can make and sell twice as many magnets next year as this year, the per-magnet cost will be reduced by $0.90. How many magnets is your company making and selling this year? Thanks. 2. Originally Posted by demo1 The question is: your company makes fridge magnets. The materials for each magnet is$0.14. Your company has additional expenses of $27 000 year. The per-magnet cost is$\displaystyle \frac{total-costs-per-year}{number-produced-per -year}$. Okay, let the number of magnets being made this year be$\displaystyle n.$The current cost per-magnet is$\displaystyle \frac{27\,000+0.14n}n.$If your company can make and sell twice as many magnets next year as this year, the per-magnet cost will be reduced by$0.90.
The cost for next year would be

$\displaystyle \frac{27\,000+0.28n}{2n}$

which is $0.90 less than the current year. Hence,$\displaystyle \frac{27\,000+0.28n}{2n}=\frac{27\,000+0.14n}n-0.9.$Multiply through by$\displaystyle n,\displaystyle 13\,500+0.14n=27\,000+0.14n-0.9n\displaystyle \Rightarrow0.9n=13\,500\displaystyle \Rightarrow n=15\,000.\$

3. Wow THANKS! That was more simple than i anticipated.