A mine $2,000,000 and is said to contain 80,000 tons of ore.When all the ore has been mined,the land can be sold for $100,000.If the book value of the mine after 3 years is $1,080,000,how many tons of ore have been mined up to that point?

Question

Quizplus · Accepted Answer

The book value of the mine after 3 years is equal to its original value minus the depletion expense over the past 3 years.

Let x be the number of tons of ore mined up to that point. 
Depletion rate = (2,000,000 - 100,000) / 80,000 = $23 of depletion per ton of ore mined.

Total depletion expense over 3 years = 1,080,000 - 2,000,000 = $920,000

Depletion expense per ton of ore = $920,000 / x

Therefore, we have: 
$23 per ton = $920,000 / x 
x = 40,000 tons

Therefore, the number of tons of ore mined up to that point is 40,000 - 1,200 (tons mined annually for 3 years) = 38,800 tons.

The closest answer choice is D, 38,737.

A Mine $2,000,000 and Is Said to Contain 80,000 Tons