Question

Sue has baked 3 different types of circular cake, all measuring 8 inches across. There are equal numbers of coffee cakes and lemon cakes, but just one carrot cake. She wants to arrange them on a rectangular table with area 576 square inches. Find the dimensions of the table. How many cakes has Sue baked? Sue would like to arrange her cakes to make an attractive display. She is a stickler for detail, so she won’t place lemon cakes directly next to the carrot cake; nor may cakes of the same flavour be next to each other. Show how she can achieve this.

Answer 1

1) suppose for purposes of calculation that the cake is inscribed in a square of 8 by 8
the area of 1 cake=8*8=64 in²
the rectangular table area=576 in²-----> I assume square table 24 in x 24 in
576/64= 9----------- > Sue has baked 9 cakes

if just 1 carrot cake
then
(9-1)=8 ---------->  coffee cakes and lemon cakes
we know that equal numbers of coffee cakes and lemon cakes
therefore
coffee cakes=8/2=4
lemon cakes=4
carrot cake=1

the answer part 1) is
the dimensions of the table are 24 in x 24 in
the answer part 2) is
Sue has baked 9 cakes
coffee cakes=4
lemon cakes=4
carrot cake=1

part 3) distribution of the cakes in the table 24  in x 24 in
answer

let
Z------->carrot cake
C------->coffee cakes
L------->lemon cakes

Z-C-L  or      C-L-C
C-L-C           Z-C-L
L-C-L           C-L-C