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 Production =$34,816
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.

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 d cost =

Answer 2

128 lawn mowers were manufactured to incur the average production cost of $660.

The average production cost can be solved through the solution:
Let n = number of lawn mowers manufactured
total cost / n = 660
total cost = 34816 + 388n
(34816 + 388n) / n = 660
Solving for n...
660n = 34816 + 388n
272n = 34816
n = 128

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