Fabian had 105 beads. ⁴₇ were purple and the rest were red and white. The ratio of the number of red beads to the number of white beads was 1 : 4. Fabian decided to give away some purple beads to decrease the number of purple beads to half of the total number of beads.

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

Purple beads	Red beads	White beads	Total
4x5	3x5
	1x3	4x3
20 u	3 u	12 u	105

	Purple beads	Red beads	White beads
Before	20 u	3 u	12 u
Change	- ?
After	15 u	15 u
Comparing purple, red and white beads in the end	1	1

(a)
The total number of red beads and white beads is repeated. Make the total number of red beads and white beads the same.  LCM of 3 and 5 is 15.

Total number of beads at first
= 20 u + 3 u + 12 u
= 35 u

35 u = 105

1 u = 105 ÷ 35 = 3

Number of more purple beads than red beads at first
= 20 u - 3 u
= 17 u
= 17 x 3
= 51

(b)
Number of more purple beads that Fabian had to give away
= 20 u - 15 u
= 5 u
= 5 x 3
= 15

Answer(s): (a) 51; (b) 15