SOLUTION: The Tie Shop sells its ties for $41 each. The shop has weekly fixed costs of $546 and each tie costs $22 to make. Let x stand for the number of ties. The Tie Shop will break e

Question 1167790: The Tie Shop sells its ties for $41 each. The shop has weekly fixed costs of $546 and each tie costs $22 to make. Let x stand for the number of ties.
The Tie Shop will break even when _______ ties are sold.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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