Algebra

 

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  

_.

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.