A price of machinery depreciates $6000 the first year, $5700 the second year, And $5400 the third year. If the rate of depreciation is constant, what is the amount of depreciation of the place of machinery in the sixth year?
A. $18,500
B. $4500
C. $36,500
D.$4800
Since the rate of depreciation is constant, we can assume that the price of machinery depreciates by the same amount each year.
Let's call that amount "x".
So, the first year, the price of machinery depreciates by $6000, which means that:
$6000 = x
Similarly, the second year, the price of machinery depreciates by $5700, which means that:
$5700 = x
And the third year, the price of machinery depreciates by $5400, which means that:
$5400 = x
Since we know that all three of these equations are equal to x, we can set them equal to each other:
$6000 = $5700 = $5400
Since all three equations are equal, we can solve for x:
6000 = 5700 = 5400
Divide both sides of the equation by 100:
60 = 57 = 54
The value of x is 54.
Therefore, the price of machinery depreciates by $5400 each year.
To find the amount of depreciation of the place of machinery in the sixth year, we need to find 6 times the yearly depreciation:
6 * $5400 = $<<6*5400=32400>>32,400
Therefore, the amount of depreciation of the place of machinery in the sixth year is $32,400.
None of the given answer choices match this amount.