Owen had 45 beads. ³₅ were brown and the rest were red and silver. The ratio of the number of red beads to the number of silver beads was 1 : 5. Owen decided to give away some brown beads to decrease the number of brown beads to half of the total number of beads.

1. How many more brown beads than red beads did he have at first?
2. How many brown beads did he have to give away?

Brown beads	Red beads	Silver beads	Total
3x3	2x3
	1x1	5x1
9 u	1 u	5 u	45

	Brown beads	Red beads	Silver beads
Before	9 u	1 u	5 u
Change	- ?
After	6 u	6 u
Comparing brown, red and silver beads in the end	1	1

(a)
The total number of red beads and silver beads is repeated. Make the total number of red beads and silver beads the same.  LCM of 2 and 6 is 6.

Total number of beads at first
= 9 u + 1 u + 5 u
= 15 u

15 u = 45

1 u = 45 ÷ 15 = 3

Number of more brown beads than red beads at first
= 9 u - 1 u
= 8 u
= 8 x 3
= 24

(b)
Number of more brown beads that Owen had to give away
= 9 u - 6 u
= 3 u
= 3 x 3
= 9

Answer(s): (a) 24; (b) 9