In March, Shannon and Valen had beads in the ratio 9 : 4. In April, each of them gave away the same number of beads. Shannon then had thrice as many beads as Valen.

1. Find the ratio of the number of beads Valen had in March to the number of beads he had in April.
2. Find the ratio of the total number of beads both had in March to the total number of beads both had in April.

	Shannon	Valen	Difference
Before	9x2 = 18 u	4x2 = 8 u	5x2 = 10 u
Change	- 3 u	- 3 u
After	3x5 = 15 u	1x5 = 5 u	2x5 = 10 u

(a)
Since Shannon and Valen gave away the same number of beads, the difference in the number of beads between Shannon and Valen at first and in the end remains the same.

Make the difference in the number of beads at first and in the end the same. LCM of 5 and 2 is 10.

Valen's beads in March : Valen's beads in April
8 : 5

(b)
Total number of beads in March
= 18 u + 8 u
= 26 u

Total number of beads in April
= 15 u + 5 u
= 20 u

Total beads in March : Total beads in April
26 : 20 _(÷2)
13 : 10 

Answer(s): (a) 8 : 5; (b) 13 : 10