Question

A lawn mower manufacturer incurs a total of $34,816 in overhead costs and $388 per lawn mower in production costs. How many lawn mowers were manufactured if the average cost of production is $660?

Answer 1

Given:
Overhead cost = 34,816
Production cost per lawn mower = 388
Average cost per lawn mower = 660

Total Production cost + Overhead Cost = Total Cost 
Total Cost ÷ # of lawn mowers produced = Average cost per lawnmower

Let x be the number of lawn mowers produced:

(388x + 34,816)/x = 660
x((388x + 34,816)/x) = x * 660
388x + 34,816 = 660x
34,816 = 660x - 388x
34,816 = 272x
34,816/272 = 272x/272
128 = x

There are 128 lawnmowers manufactured.

To check:
388x + 34,816 = total production cost.
388(128) + 34,816 = 49,664 + 34,816 = 84,480

84,480 ÷ 128 = 660 ave cost per unit