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. The data is given as follows:

x (boxes) y (inches)
26 412
51 515
61 618

What is the constant of proportionality? Write your answer as a whole number or decimal, in inches per box.

Answer 1

The constant of proportionality in this scenario is approximately 15.85 inches per box.

Step-by-step explanation:

In a proportional relationship, the constant of proportionality represents the rate at which one quantity changes in relation to another quantity. To find the constant of proportionality in this scenario, we can use the formula y = kx, where y represents the amount of shelf space and x represents the number of cereal boxes. We can choose any set of data points from the given information and plug them into the formula to solve for k. Let's use the first data point (26, 412):

412 = 26k. Solving for k, we get k = 412/26 = 15.85. Therefore, the constant of proportionality is approximately 15.85 inches per box.