Worded Algebra

Question

Three tank: A, B and C are used to store oil.

Tank A contains n litres of oil. Tank B contains (n+150) litres of oil. Tank C is empty.

Oil is pumped from Tank A and from Tank B into Tank C so that all three tanks contain the same amount of oil. 500 litres of oil are pumped from Tank A to Tank C.

Work out the value of n.

Answer 1

Okay, this question messed with my head a bit.  I was thinking that if they were all equal (at the end), and the C tank had 500 and the A tank lost 500, then it made the math impossible...  

 

Consider the total amount of oil in all of the tanks is constant.

 

TankA+TankB+TankC=Total

 

Now we can compare the two conditions: initial and final.  The part that was messing with me is that we have an undefined variable: the amount from B that was moved to C.  I called it "x".

 

Original:

(n)+(n+150)+0=Total

 

Final:
(n-500)+(n+150-x)+(500+x)=Total

 

Now, in this final condition, we know that all tanks are equal, so we can write a series of equations:

Tank A = Tank B (use to solve for x)

n-500=n+150-x

 

Tank A=Tank C (substitute x and solve for n)

n-500=500+x

 

The final answer for n is between 1500 and 1800 L.

Answer 2

If 500 litres are pumped from tank A, then to keep A and B at the same final level then 500 + 150 litres must be pumped from B.

 

This means that the total volume in C would be 500 + 500 + 150 = 1150 litres

 

This volume must now be the same for each tank A, B and C = 1150 each.

 

consider tank A; n - 500 = 1150 ; therefore n = 1650 litres

 

and tank B initially contained n + 150 = 1800 litres

 

check ; A gave up 500 leaving     1150

           B gave up 650 leaving     1150

           C received 500+650    =  1150    (proven)