Ahmad had 100 beads. ³₅ were black and the rest were yellow and purple. The ratio of the number of yellow beads to the number of purple beads was 1 : 4. Ahmad decided to give away some black beads to decrease the number of black beads to half of the total number of beads.

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

Black beads	Yellow beads	Purple beads	Total
3x5	2x5
	1x2	4x2
15 u	2 u	8 u	100

	Black beads	Yellow beads	Purple beads
Before	15 u	2 u	8 u
Change	- ?
After	10 u	10 u
Comparing black, yellow and purple beads in the end	1	1

(a)
The total number of yellow beads and purple beads is repeated. Make the total number of yellow beads and purple beads the same.  LCM of 2 and 5 is 10.

Total number of beads at first
= 15 u + 2 u + 8 u
= 25 u

25 u = 100

1 u = 100 ÷ 25 = 4

Number of more black beads than yellow beads at first
= 15 u - 2 u
= 13 u
= 13 x 4
= 52

(b)
Number of more black beads that Ahmad had to give away
= 15 u - 10 u
= 5 u
= 5 x 4
= 20

Answer(s): (a) 52; (b) 20