Fascinated by ocean life, Trent wants to put a saltwater aquarium in his bedroom. He needs to make sure he buys a big enough tank to grow his collection of fish over time.

Question

This table shows the relationship between the number of fish in Trent's collection, x, and the smallest tank size (in gallons), y, he needs to safely keep his fish.
x (fish) y (gallons)
1 17
2 34
3 51
5 85
According to the values in the table, do x and y have a proportional relationship?
yes
no
What is the constant of proportionality? Write your answer as a whole number or decimal.
gallons per fish

Answer 1

To determine if \( x \) (the number of fish) and \( y \) (the gallons needed for the tank) have a proportional relationship, we need to see if the ratio \(\frac{y}{x}\) is constant for the values given in the table.

Let's calculate the ratio for each pair of values:

1. When \( x = 1 \): \[ \frac{y}{x} = \frac{17}{1} = 17 \]

2. When \( x = 2 \): \[ \frac{y}{x} = \frac{34}{2} = 17 \]

3. When \( x = 3 \): \[ \frac{y}{x} = \frac{51}{3} = 17 \]

4. When \( x = 5 \): \[ \frac{y}{x} = \frac{85}{5} = 17 \]

Since the ratio \(\frac{y}{x}\) is consistently 17 for each pair, we can conclude that \( x \) and \( y \) do have a proportional relationship.

Answer: Yes.

Constant of proportionality: 17 gallons per fish.