Question

At a birthday party, there are cupcakes. The number of cupcakes, c, each guest receives varies inversely as the number of guests,

G. If 52 guests each receive 4 cupcakes, how many cupcakes would 13 guests each receive?"

A) 16
B) 26
C) 52
D) 104

Answer 1

In an inverse variation, the number of cupcakes each guest receives is inversely proportional to the number of guests. To find the number of cupcakes 13 guests would receive, we can use the formula c = k/G, where k is the constant of variation. By finding the value of k and plugging in 13 for G, we can determine that each guest would receive 16 cupcakes.

Step-by-step explanation:

In an inverse variation, the product of the two variables remains constant. In this case, the number of cupcakes, c, each guest receives is inversely proportional to the number of guests, G. We can express this relationship as c = k/G, where k is the constant of variation.

To find the value of k, we can use the given information: when there are 52 guests, each guest receives 4 cupcakes. Plugging these values into the equation, we have 4 = k/52. Solving for k, we get k = 208.

Now we can use this value of k to find the number of cupcakes each guest would receive when there are 13 guests. Substituting 13 for G in the equation c = 208/G, we get c = 208/13 = 16. Therefore, when there are 13 guests, each guest would receive 16 cupcakes.