The total number of beads in Bag L, Bag M and Bag N was 48.
78 of the beads from Bag L and 4 beads from Bag M were removed. More beads were then added into Bag N until the number of beads in it was quadrupled. The ratio of the number of beads in Bag L to Bag M to Bag N became 1 : 2 : 4.
- How many less beads were there in Bag M than Bag L at first?
- Find the total number of beads in Bag M and Bag N in the end.
|
Bag L |
Bag M |
Bag N |
Total |
Before |
8 u |
2 u + 4 |
1 u |
48 |
Change |
- 7 u |
- 4 |
+ 3 u |
|
After |
1 u |
|
4 u |
|
Comparing the beads in the end |
1 u |
2 u |
4 u |
|
(a)
Total number of beads at first
= 8 u + 2 u + 4 + 1 u
= 11 u + 4
11 u + 4 = 48
11 u = 48 - 4
11 u = 44
1 u = 44 ÷ 11 = 4
Number of less beads in Bag M than Bag L at first
= 8 u - (2 u + 4)
= 8 u - 2 u - 4
= 6 u - 4
= 6 x 4 - 4
= 24 - 4
= 20
(b)
Total number of beads in Bag M and Bag N in the end
= 2 u + 4 u
= 6 u
= 6 x 4
= 24
Answer(s): (a) 20; (b) 24