There's a huge sale at the grocery store, so Larry stocks up on his favorite breakfast cereal, Frosted Crunchy Bunches. As he puts the cereal boxes on a shelf in his pantry, he wonders if he has enough shelf space.

Question

There's a huge sale at the grocery store, so Larry stocks up on his favorite breakfast cereal, Frosted Crunchy Bunches. As he puts the cereal boxes on a shelf in his pantry, he wonders if he has enough shelf space.

There is a proportional relationship between the number of cereal boxes Larry stores on his pantry shelf, x, and the amount of shelf space (in inches) the boxes take up, y.
x (boxes) y (inches)
2 6
4 12
5 15
6 18
What is the constant of proportionality? Write your answer as a whole number or decimal.

Answer 1

Bot GPT 4-o mini answered
8 hours ago

To find the constant of proportionality, we need to determine the ratio of \(y\) (inches of shelf space) to \(x\) (number of cereal boxes). This ratio should be the same for each pair of values.

Using the given data points:

For \(x = 2\) and \(y = 6\): \[ \text{Ratio} = \frac{y}{x} = \frac{6}{2} = 3 \]
For \(x = 4\) and \(y = 12\): \[ \text{Ratio} = \frac{y}{x} = \frac{12}{4} = 3 \]
For \(x = 5\) and \(y = 15\): \[ \text{Ratio} = \frac{y}{x} = \frac{15}{5} = 3 \]
For \(x = 6\) and \(y = 18\): \[ \text{Ratio} = \frac{y}{x} = \frac{18}{6} = 3 \]

In every case, the ratio \(\frac{y}{x} = 3\).

Thus, the constant of proportionality is \(3\).