The total number of balls in Bag E, Bag F and Bag G was 76.
78 of the balls from Bag E and 11 balls from Bag F were removed. More balls were then added into Bag G until the number of balls in it was quadrupled. The ratio of the number of balls in Bag E to Bag F to Bag G became 1 : 4 : 4.
- How many more balls were there in Bag E than Bag F at first?
- Find the total number of balls in Bag E and Bag G in the end.
|
Bag E |
Bag F |
Bag G |
Total |
Before |
8 u |
4 u + 11 |
1 u |
76 |
Change |
- 7 u |
- 11 |
+ 3 u |
|
After |
1 u |
|
4 u |
|
Comparing the balls in the end |
1 u |
4 u |
4 u |
|
(a)
Total number of balls at first
= 8 u + 4 u + 11 + 1 u
= 13 u + 11
13 u + 11 = 76
13 u = 76 - 11
13 u = 65
1 u = 65 ÷ 13 = 5
Number of more balls in Bag E than Bag F at first
= 8 u - (4 u + 11)
= 8 u - 4 u - 11
= 4 u - 11
= 4 x 5 - 11
= 20 - 11
= 9
(b)
Total number of balls in Bag E and Bag G in the end
= 1 u + 4 u
= 5 u
= 5 x 5
= 25
Answer(s): (a) 9; (b) 25