Step-by-step explanation:

To find out how many plates can be used to arrange the 90 cupcakes, we need to determine the factors of 90. Factors are numbers that divide evenly into another number without leaving a remainder.

The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.

Since Emily wants to arrange the cupcakes in such a way that every plate carries an equal number of cupcakes, we are looking for factors that are divisible into 90 without leaving a remainder.

Therefore, the possible numbers of cupcakes per plate would be 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.

Emily can use any of these numbers as the number of cupcakes per plate. Each number represents a different arrangement of cupcakes, with a varying number of plates.

For example, if Emily decides to have 10 cupcakes per plate, she would need 9 plates (90 cupcakes ÷ 10 cupcakes per plate = 9 plates).

Ultimately, the number of plates that can be used for this arrangement depends on the desired number of cupcakes per plate.

NUMBER OF CAKES EMILY HAD=90

THE NUMBER OF PLATES NEEDED=X

we will find the highest common factor.

H.C.F.=

2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90

HENCE,

2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90

ANY NUMBER OF PLATES AMONG THESE CAN BE USED