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.
400 T * 1.0 oz/T * $1625 / oz
To find the value of the gold in each truck, we need to multiply the weight of the gold ore in each truck by the price of gold per ounce.
First, we convert the weight of the gold ore from tons to ounces. Since we are given that each ton of gold ore contains 1.0 ounce of gold, multiplying the weight of the gold ore in tons by 1.0 ounce/ton gives us the weight of the gold in each truck in ounces.
Next, we multiply the weight of the gold in each truck (in ounces) by the price of gold per ounce to find the value of the gold in each truck.
Let's break it down step by step using dimensional analysis:
1. Start with the weight of the gold ore in each truck:
- Given: 400 tons
- Conversion factor: 1.0 ounce/ton
Multiply:
400 tons x (1.0 ounce/ton) = 400 ounces of gold
2. Calculate the value of the gold in each truck:
- Given: Price of gold today = $1625 per ounce
Multiply:
400 ounces x $1625/ounce = $650,000
Therefore, the value of the gold in each truck is $650,000.