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.

Answer 1

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

Let's calculate the ratios for each pair:

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

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

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

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

Since the ratio \( \frac{y}{x} \) is consistently 17 for all values of \( x \), \( x \) and \( y \) do have a proportional relationship.

Answer:

Yes, they have a proportional relationship. The constant of proportionality is 17.