Question

liz just bought a new fish tank. As she fills it with water, the weight changes.
There is a linear relationship between the amount of water in the tank, in liters, and the weight of the tank, in kilograms.
Amount of water (liters) Weight of the tank (kilograms)
10 40
30 60
50 80
Describe the rate of change for this relationship.
The weight of the tank
by
per liter of water.

Answer 1

To determine the rate of change for the relationship between the amount of water in liters and the weight of the tank in kilograms, we can analyze the data points given.

1. From the data:
- When the amount of water is 10 liters, the weight is 40 kg.
- When the amount of water is 30 liters, the weight is 60 kg.
- When the amount of water is 50 liters, the weight is 80 kg.

2. We can calculate the weight change for every 10 liters of water added:
- From 10 liters to 30 liters: 60 kg - 40 kg = 20 kg (weight change)
- From 30 liters to 50 liters: 80 kg - 60 kg = 20 kg (weight change)

3. The amount of water added in each case is 20 liters (30 liters - 10 liters, and 50 liters - 30 liters).

Thus, the rate of change can be calculated as:

\[
\text{Rate of change} = \frac{\text{Change in weight (kg)}}{\text{Change in amount of water (liters)}} = \frac{20 \text{ kg}}{20 \text{ liters}} = 1 \text{ kg per liter}
\]

Therefore, the weight of the tank **increases by 1 kilogram per liter of water**.