Question

A rectangular tank containing some pebbles was 80% filled with water.When all the pebbles were removed, the water level dropped to 25% of its original height.The volume of the water left in the tank was 3 litres.
a)Find the capacity of the tank.

b)If the volume of each pebble is 60 cm3,how many pebbles were there in the tank.

Answer 1

Task:

A rectangular tank containing some pebbles was 80% filled with water. When all the pebbles were removed, the water level dropped to 25% of its original height. The volume of the water left in the tank was 3 liters.

a) Find the capacity of the tank.

b) If the volume of each pebble is 60 cm³, how many pebbles were there in the tank?

Solution:

Let the capacity of the tank is $x$ liters and the volume of all pebbles is $y$. Then volume of all pebbles and the water is $3 + y$ and it equals to 80% capacity of the tank: $3 + y = 80 \cdot \frac{x}{100}$.

The volume of the water left in the tank is equals to 25% capacity of the tank: $3 = 25 \cdot \frac{x}{100}$.

We have obtained a system of equations:

$$\left\{ \begin{array}{l} 3 + y = 80 \cdot \frac{x}{100} \\ 3 = 25 \cdot \frac{x}{100} \end{array} \right.$$

Solve it:

$$\left\{ \begin{array}{l} 3 + y = 80 \cdot \frac{x}{100} \left\{ \begin{array}{l} 3 + y = 0.8x \\ 3 = 0.25x \end{array} \right. \begin{array}{l} y = 0.8x - 3 \\ \frac{3}{0.25} = \frac{0.25x}{0.25} \end{array} \left\{ \begin{array}{l} y = 0.8(12) - 3 \\ 12 = x \end{array} \right. \begin{array}{l} y = 9.6 - 3 \\ x = 12 \end{array} \left\{ \begin{array}{l} y = 6.6 \\ x = 12 \end{array} \right. \end{array} \right.$$

(a)

Capacity of the tank is 12 liters.

(b)

1 cubic centimeter = 0.001 liters. So volume of each pebble is $60 \, \text{cm}^3 = 60 \cdot 0.001 \, l = 0.06l$.

Amount of pebbles is $\frac{6.6l}{0.06l} = 110$.

Answer: (a) 12 liters and (b) 110.