If gold sells today for 1625 per ounce, and a large mining truck hauls 400 tons of gold ore, what is the value of the gold in each truck if each ton of gold ore contains 1.0 ounces of gold? Use dimensional analysis.
1625 * 400 since 400 tons of gold ore is 400 ounces of gold
5.5
To determine the value of the gold in each truck, we need to use dimensional analysis.
Step 1: Convert the weight of the gold ore from tons to ounces.
1 ton = 2000 pounds (since 1 ton = 2000 lbs)
1 pound = 16 ounces (since 1 lb = 16 oz)
So, 1 ton = 2000 * 16 = 32000 ounces
Step 2: Calculate the total weight of gold in each truck.
Each ton of gold ore contains 1.0 ounce of gold.
Since each truck hauls 400 tons of gold ore, the total weight of gold in each truck is 400 * 1.0 = 400 ounces.
Step 3: Calculate the value of the gold in each truck.
Given that the selling price of gold is $1625 per ounce, we can find the value of the gold in each truck by multiplying the total weight of gold in each truck (400 ounces) by the selling price per ounce ($1625).
Value of gold in each truck = 400 ounces * $1625/ounce
Now, just multiply the two values to find the answer using a calculator or manipulating the units:
Value of gold in each truck = 400 * $1625 = $650,000
Therefore, the value of the gold in each truck would be $650,000.