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

1. Find the ratio of the number of beads Howard 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.

	Yen	Howard	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 Yen and Howard gave away the same number of beads, the difference in the number of beads between Yen and Howard 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.

Howard's beads in April : Howard'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