Fred had 75 beads. ⁴₅ were yellow and the rest were brown and gold. The ratio of the number of brown beads to the number of gold beads was 1 : 2. Fred 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 brown beads did he have at first?
2. How many yellow beads did he have to give away?

Yellow beads	Brown beads	Gold beads	Total
4x3	1x3
	1x1	2x1
12 u	1 u	2 u	75

	Yellow beads	Brown beads	Gold beads
Before	12 u	1 u	2 u
Change	- ?
After	3 u	3 u
Comparing yellow, brown and gold beads in the end	1	1

(a)
The total number of brown beads and gold beads is repeated. Make the total number of brown beads and gold beads the same.  LCM of 1 and 3 is 3.

Total number of beads at first
= 12 u + 1 u + 2 u
= 15 u

15 u = 75

1 u = 75 ÷ 15 = 5

Number of more yellow beads than brown beads at first
= 12 u - 1 u
= 11 u
= 11 x 5
= 55

(b)
Number of more yellow beads that Fred had to give away
= 12 u - 3 u
= 9 u
= 9 x 5
= 45

Answer(s): (a) 55; (b) 45