In April, Diana and Caden had beads in the ratio 8 : 3. In May, each of them gave away the same number of beads. Diana then had five times as many beads as Caden.

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

	Diana	Caden	Difference
Before	8x4 = 32 u	3x4 = 12 u	5x4 = 20 u
Change	- 7 u	- 7 u
After	5x5 = 25 u	1x5 = 5 u	4x5 = 20 u

(a)
Since Diana and Caden gave away the same number of beads, the difference in the number of beads between Diana and Caden 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 4 is 20.

Caden's beads in April : Caden's beads in May
12 : 5

(b)
Total number of beads in April
= 32 u + 12 u
= 44 u

Total number of beads in May
= 25 u + 5 u
= 30 u

Total beads in April : Total beads in May
44 : 30 _(÷2)
22 : 15 

Answer(s): (a) 12 : 5; (b) 22 : 15