A fuel tanker weighs 2500 tons when 25% full and 3100 tons when 75% full. What is its weight in tons when empty?

Guest Jul 6, 2022

#1**0 **

*A fuel tanker weighs 2500 tons when 25% full and 3100 tons when 75% full. What is its weight in tons when empty?*

I'll make a little table so it's easy to visualize.

% Full Weight (tons)

0 **2200**

25 2500

50 **2800**

75 3100

100 **3400** (Values in maroon are interpolated from the given data.)

From 25% to 75% the weight goes from 2500 to 3100

The change in fullness is 50% and the change in weight is 600

Half of 50 is 25 and half of 600 is 300

So every 25% of the tank changes the weight by 300 tons

We subtract those 300 tons from the weight when 25% full, thus: **2500 – 300 = 2200**

Therefore, the weight of the empty tanker is **2200 tons**

_{.}

Guest Jul 6, 2022

#2**0 **

Let the weight of the empty tank ==E

Let the weight of fuel when tank is full ==F

E + 0.25F ==2,500.....................(1)

E + 0.75F ==3,100......................(2), solve for E, F

Subtract (1) from (2), and we have:

0.50F ==600

**F ==600 / 0.50 ==1,200 tons - weight of fuel when tank is full**

Sub this into (1) above:

E + [0.25 * 1200] ==2,500

E + 300 == 2,500

**E ==2,500 - 300 ==2,200 tons - weight of the empty tank.**

Guest Jul 6, 2022