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Answer :
Based on the given information, we can solve for the weight of the empty fuel tanker and the weight of the fuel. Let's denote the empty tanker's weight as "x" and the weight of the fuel when 100% full as "y."
When the fuel tanker is 25% full, the total weight (x + 0.25y) is 2500 tons. And when it's 75% full, the total weight (x + 0.75y) is 3700 tons. We can write this as a system of linear equations:
1. x + 0.25y = 2500
2. x + 0.75y = 3700
To solve this system, we can eliminate "x" by subtracting equation 1 from equation 2:
0.5y = 1200
Now, we can solve for "y":
y = 2400 tons
Using the value of "y," we can find the value of "x" from either equation 1 or 2. We'll use equation 1:
x + 0.25(2400) = 2500
x + 600 = 2500
x = 1900 tons
So, the empty fuel tanker weighs 1900 tons, and the weight of the fuel when 100% full is 2400 tons.
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