How Much water can a tank hold?

Question

At Sonia’s house there are two water tanks. One tank can hold $500$ litres more than the smaller tank. When the smaller tank is $2/3$ full it holds as much water as half the larger tank. What is the capacity of the largest tank?

Answer 1

Put $b,s$ be the max capacity of the larger, and smaller tanks. Then: $b = s+500, \dfrac{2s}{3} = \dfrac{b}{2}$. Substitute $s+500$ for $b$ in the second equation to get: $\dfrac{2s}{3} = \dfrac{s+500}{2}\implies s = 1,500, b = 2,000$ liters respectively.

Answer 2

HINT: Let $V$ be the volume of the large tank and $v$ be the volume of the smaller tank. Then from the problem, you can derive that $$V=v+500$$ $$\frac{1}{2}V=\frac{2}{3}v$$ Can you solve this system of equations?