Question

Four machines, each costing $5,700, were purchased for an office. Each machine requires
the service of an operator at a salary of $1,100 per month. These machines are to replace 8
clerks, two of whom each earn $750 per month, three of whom each earn $650 per month,
and three of whom each earn $950 per month. How many months will it take to recover the
cost of the machines?
A.
B.
C.
D.
10 months
11 months
12 months
More than 12 months

Answer 1

The number of months it would take to recover the cost of the machines is 12 months.

What is the total cost of the machines and the salary of the operators?

Total cost of the four machines = $5700 x 4 = $22,800

The total salaries of the machine operators in t months = 4t x $1,00 = $4,400t

Total cost = $22,800 +  $4,400t

What is the amount saved by replacing the 8 clerks in t months?

($750 x 2t) + ($650 x 3t) + ($950 x 3t)

= $1500t + $1,950t +$2,850t

= $6300t

In how many months would it take to recover the cost of the machines?

$22,800 +  $4,400t  =  $6300t

Combine similar terms

$22,800 = $6300t - $4400t

$22,800 = $1900t

Divide both sides by 1900

t = 12 months

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