SOLUTION: Old-Tyme Fashions specializes in hats modelled after fashions from the past. It purchases these hats for $42 each. It can provide a custom service to print the new owner’s name o

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Old-Tyme Fashions specializes in hats modelled after fashions from the past. It purchases these hats for $42 each. It can provide a custom service to print the new owner’s name o      Log On


   

Question 1136532: Old-Tyme Fashions specializes in hats modelled after fashions from the past. It purchases these hats for $42 each. It can provide a custom service to print the new owner’s name on the hatband. The printing machine costs $243 per month to rent. If Old-Tyme sells the hats at a price of $69 each, how many does it need to sell to break even?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.
The cost function to make n hats is


    C(n) = 42*n + 243   dollars.


The revenue function is


    R(n) = 69*n  dollars.


The break event equation/inequality is


    R(n) >= C(n),   or

    69*n >= 243 + 42*n.


Simplify and solve for n:


    (69-42)*n >= 243

    27n >= 243  ===============>  n >= 243/27 = 9.


ANSWER. 9 hats.

Solved.


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Each hat costs them $42; they sell them for $69; they make a profit of $27 on each hat.

The number of hats they need to sell to offset the $243 rent is 243/27 = 9.