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# Yellow and pink yarn balls are sold in either Package A or Package B. Each package contains the same number of yarn balls.

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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?

Oct 21, 2020

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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

Oct 21, 2020