The total number of beads in Basket Q, Basket R and Basket S was 119. ⁷₈ of the beads from Basket Q and 2 beads from Basket R were removed. More beads were then added into Basket S until the number of beads in it was doubled. The ratio of the number of beads in Basket Q to Basket R to Basket S became 1 : 4 : 2.

1. How many less beads were there in Basket R than Basket Q at first?
2. Find the total number of beads in Basket R and Basket S in the end.

	Basket Q	Basket R	Basket S	Total
Before	8 u	4 u + 2	1 u	119
Change	- 7 u	- 2	+ 1 u
After	1 u		2 u
Comparing the beads  in the end	1 u	4 u	2 u

(a)
Total number of beads at first
= 8 u + 4 u + 2 + 1 u
= 13 u + 2

13 u + 2 = 119
13 u = 119 - 2
13 u = 117

1 u = 117 ÷ 13 = 9

Number of less beads in Basket R than Basket Q at first 
= 8 u - (4 u + 2)
= 8 u - 4 u - 2
= 4 u - 2
= 4 x 9 - 2
= 36 - 2
= 34

(b)
Total number of beads in Basket R and Basket S in the end
= 4 u + 2 u
= 6 u
= 6 x 9
= 54 

Answer(s): (a) 34; (b) 54