The total number of beads in Bag E, Bag F and Bag G was 86.
38 of the beads from Bag E and 2 beads from Bag F were removed. More beads were then added into Bag G until the number of beads in it was doubled. The ratio of the number of beads in Bag E to Bag F to Bag G became 5 : 3 : 2.
- How many more beads were there in Bag E than Bag F at first?
- Find the total number of beads in Bag E and Bag G in the end.
|
Bag E |
Bag F |
Bag G |
Total |
Before |
8 u |
3 u + 2 |
1 u |
86 |
Change |
- 3 u |
- 2 |
+ 1 u |
|
After |
5 u |
|
2 u |
|
Comparing the beads in the end |
5 u |
3 u |
2 u |
|
(a)
Total number of beads at first
= 8 u + 3 u + 2 + 1 u
= 12 u + 2
12 u + 2 = 86
12 u = 86 - 2
12 u = 84
1 u = 84 ÷ 12 = 7
Number of more beads in Bag E than Bag F at first
= 8 u - (3 u + 2)
= 8 u - 3 u - 2
= 5 u - 2
= 5 x 7 - 2
= 35 - 2
= 33
(b)
Total number of beads in Bag E and Bag G in the end
= 5 u + 2 u
= 7 u
= 7 x 7
= 49
Answer(s): (a) 33; (b) 49