The ratio of the number of wafers in Container A to the number of wafers in Container B was 7 : 3. 30% of the wafers in Container A and 0.9 of those in Container B were mango. After transferring the wafers between the 2 containers, the number of cherry wafers in both containers are the same. Likewise, the number of mango wafers in both containers are the same. If a total of 260 wafers were moved, how many more wafers were there in Container A than Container B at first?
Container A |
Container B |
7 u |
3 u |
Mango |
Cherry |
Mango |
Cherry |
2.1 u |
4.9 u |
2.7 u |
0.3 u |
+ 0.3 u |
- 2.3 u |
- 0.3 u |
+ 2.3 u |
2.4 u |
2.6 u |
2.4 u |
2.6 u |
Number of mango wafers in Container A
= 30% x 7 u
=
30100 x 7 u
= 2.1 u
Number of cherry wafers in Container A
= 7 u - 2.1 u
= 4.9 u
Number of mango wafers in Container B
= 0.9 x 3 u
= 2.7 u
Number of cherry wafers in Container B
= 3 u - 2.7 u
= 0.3 u
Number of mango wafers in each container in the end
= (2.1 u + 2.7 u) ÷ 2
= 4.8 u ÷ 2
= 2.4 u
Number of cherry wafers in each container in the end
= (4.9 u + 0.3 u) ÷ 2
= 5.2 u ÷ 2
= 2.6 u
Number of wafers moved
= 0.3 u + 2.3 u
= 2.6 u
2.6 u = 260
1 u = 260 ÷ 2.6 = 100
Number of more wafers in Container A than Container B at first
= 7 u - 3 u
= 4 u
= 4 x 100
= 400
Answer(s): 400