Selling Gravel

Algebra Level 3

A quarry wants to sell a large pile of gravel. At full price, the gravel would sell for 3200 dollars. But during the first week the quarry only sells 60% of the gravel at full price. The following week the quarry drops the price by 10%, and, again, it sells 60% of the remaining gravel. Each week, thereafter, the quarry reduces the price by another 10% and sells 60% of the remaining gravel. This continues until there is only a handful of gravel left. How many dollars does the quarry collect for the sale of all its gravel?

The answer is 3000.

1 solution

Mitchell Price
Apr 23, 2014

We know that for the first sale of the gravel, this will cost: .60 * 3200 for the second sale of the gravel, we see that this will rake in: .40 (the remaining percentage) * .60 (the percentage of this sale that will be purchased) * 3200 (the original value of the gravel) * .90 (to account for the 10% decrease in value)

in other words, our total equals: $.60\quad \times \quad 3200\quad +\quad .60\times 3200\times .40\times .90\quad +\quad .60\times 3200{ (.40\times .90) }^{ 2 }+.....$

This, of course can be turned into an infinite geometric sum:

$\sum _{ i\quad =\quad 1 }^{ \infty }{ 1920{ (.36) }^{ i-1 }\quad =\quad \frac { 1920 }{ 1-.36 } =\quad 3000 }$

Selling Gravel

The answer is 3000.

1 solution

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