Archie had 240 beads. ⁴₅ were yellow and the rest were silver and green. The ratio of the number of silver beads to the number of green beads was 1 : 3. Archie decided to give away some yellow beads to decrease the number of yellow beads to half of the total number of beads.

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

Yellow beads	Silver beads	Green beads	Total
4x4	1x4
	1x1	3x1
16 u	1 u	3 u	240

	Yellow beads	Silver beads	Green beads
Before	16 u	1 u	3 u
Change	- ?
After	4 u	4 u
Comparing yellow, silver and green beads in the end	1	1

(a)
The total number of silver beads and green beads is repeated. Make the total number of silver beads and green beads the same.  LCM of 1 and 4 is 4.

Total number of beads at first
= 16 u + 1 u + 3 u
= 20 u

20 u = 240

1 u = 240 ÷ 20 = 12

Number of more yellow beads than silver beads at first
= 16 u - 1 u
= 15 u
= 15 x 12
= 180

(b)
Number of more yellow beads that Archie had to give away
= 16 u - 4 u
= 12 u
= 12 x 12
= 144

Answer(s): (a) 180; (b) 144