<PRE><B>Question 1167790</B>
r = 41 * x
c = 22 * x + 546


break even is when r = c


this becomes 41 * x = 22 * x + 546


subtract 22 * x from both sides of the equation to get:


41 * x - 22 * x = 56


simplify to get:


19 * x = 56


solve for x to get:


at x = 28.73684211
revenue is 28.73684211 * 41 = 1178.210526
cost is 546 + 28.73684211 * 22 = 1178.210526
revenue is the same as cost

 


at x = 28:
revenue is 28 * 41 = 1148
cost is 546 + 28 * 22 = 1162
revenue is less than cost.


at x = 39:
revenue is 29 * 41 = 1189
cost is 546 + 29 * 22 = 1184
revenue is greater than cost.


your solution is that the tie shop will break even when 28.73684211 ties are sold.


both numbers are close enough to 28.73684211.
29 is closer, so if you had to pick an integer, go with 29.


other than that, you can say that the shop will break even when an average of 28.73684222 ties are sold each week.


this implies that, over many weeks, an average of 28.73684211 ties were sold each week.





</PRE>