Sasha is cutting a cake into 42 equal-sized pieces. If 14 people want cake, then they can each have 3 slices. And if 21 people want cake, then they can each have 2 slices. What is the constant of proportionality in this inverse variation?

k = 42

the constant of proportionality in this inverse variation is 42.

Step-by-step explanation:

Let x represent the number of people that want cake

And y the number of slices each can have;

Since x is inversely proportional to y;

x = k/y ... 1

Where k is the proportionality constant;

To solve for k, we will substitute any of the case scenario given into equation 1.

If 14 people want cake, then they can each have 3 slices;

x = 14, y = 3

substituting;

14 = k/3

k = 14 * 3 = 42

k = 42

the constant of proportionality in this inverse variation is 42.

Therefore,

x = 42/y