Yellow and pink yarn balls are sold in either Package $A$ or Package $B$. Each package contains the same number of yarn balls.
The ratio between the numbers of yellow and pink yarn balls in Package $A$ is $2:3.$
The ratio between the numbers of yellow and pink yarn balls in Package $B$ is $3:4.$
The ratio between the numbers of Package $A$ and Package $B$ in the store is $4:5.$
What is the ratio between the numbers of yellow and pink yarn balls in all these packages combined?
Here is my attempt at your question:
p/y =2/3
2/5 * N =2/5N pink
3/5 * N =3/5N yellow
p/y = 3/4
3/7 * N =3/7N pink
4/7 * N =4/7N yellow
4/9 * M =4/9M packages A
5/9 * M =5/9M packages B
(4/9M * 2/5N) + (4/9M * 3/7N) =116 / 315NM
(5/(9M) * 3/(5N)) + (5/(9M) * 4/(7N)) =41 / 63NM
116 / (315NM) / 41 / (63NM) =7308 / 12915
Total Ratio of: Pink yarn balls / Yellow yarn balls
7308 / 12915 = 116 / 205
