Working on a school project

Question

Mindy and Troy combined ate   pieces of the wedding cake. Mindy ate   pieces of cake and Troy had   of the total cake. Find the total number of pieces of cake.

Answer 1

Mindy ate x pieces of the cake

Troy ate 1/y part of the cake

together they ate the entire cake.

how many pieces were there in the cake? assuming each piece was the same size.

take a specific example. Mindy ate 2 pieces. Troy ate 1/2 the cake. then 2 pieces is half the cake, and total pieces in the cake are 4 pieces.

now change 2 to x, and the second 2 to y

Mindy ate x pieces, if Troy ate 1/2 the cake, then total pieces are 2x

if Troy ate 1/y th of the cake, then total pieces are xy/(y-1) pieces

Answer: xy/(y-1) pieces of the cake.

let's say Mindy ate 2 pieces and Troy ate 1/4 the cake, then 2 = 3/4 of the cake, remaining 1/4 = 2/3 piece for Troy, total 2 2/3 pieces