Question

Prospectors are considering searching for gold on a plot of land that has 2.38 x 10^3 cubic ft of soil. If the soil contains 1.31 g of gold per bucket of soil, the volume of the bucket is 4.67L and the price of gold is $1639/oz, how much will the prospectors make?

Answer 1

1. we need to convert 2.38 x 10^3 cubic ft of soil to L of soil

We must use that 1 L = 0.0353 cubic ft

Then,

`2.38\cdot10^3ft^3\cdot(1L)/(0.0353ft^3)=67422.0963L`

So, the land has 67422.0963 L of soil.

2. If the volume of the bucket is 4.67 L, we need to find how many buckets there are in the number of L of soil found in the previous step.

To find this, we must divide 67422.0963 L by 4.67 L

`(67422.0963L)/(4.67L)=14437.2797`

So, there are 14437.2797 buckets of soil in the land.

3. If the soil contains 1.31 g of gold per bucket of soil, we need to find how many grams of gold there are in the number of buckets of soil found in the previous step.

To find this, we must multiply 1.31 g of gold by 14437.2797

`1.31g\cdot14437.2797=18912.8364g`

So, in the land there are 18912.8364 g of gold

4. Finally, if the price of gold is $1639/oz we must convert the grams of gold found in the previous step to oz

We must use that 1 g = 0.0353 oz

Then,

`18912.8364g\cdot(0.0353oz)/(1g)=668.6231oz`

Now, if there are 668.6231 oz of gold and the price of gold is $1639/oz, the prospectors will make

`668.6231oz\cdot(1639)/(oz)=1095873.261`

ANSWER:

The prospectors will make $1095873.261