The ratio of the number of wafers in Container E to the number of wafers in Container F was 9 : 5. 20% of the wafers in Container E and 0.6 of those in Container F were peach. After transferring the wafers between the 2 boxes, the number of cherry wafers in both boxes are the same. Likewise, the number of peach wafers in both boxes are the same. If a total of 240 wafers were moved, how many more wafers were there in Container E than Container F at first?
Container E |
Container F |
9 u |
5 u |
Peach |
Cherry |
Peach |
Cherry |
1.8 u |
7.2 u |
3 u |
2 u |
+ 0.6 u |
- 2.6 u |
- 0.6 u |
+ 2.6 u |
2.4 u |
4.6 u |
2.4 u |
4.6 u |
Number of peach wafers in Container E
= 20% x 9 u
=
20100 x 9 u
= 1.8 u
Number of cherry wafers in Container E
= 9 u - 1.8 u
= 7.2 u
Number of peach wafers in Container F
= 0.6 x 5 u
= 3 u
Number of cherry wafers in Container F
= 5 u - 3 u
= 2 u
Number of peach wafers in each box in the end
= (1.8 u + 3 u) ÷ 2
= 4.8 u ÷ 2
= 2.4 u
Number of cherry wafers in each box in the end
= (7.2 u + 2 u) ÷ 2
= 9.2 u ÷ 2
= 4.6 u
Number of wafers moved
= 0.6 u + 2.6 u
= 3.2 u
3.2 u = 240
1 u = 240 ÷ 3.2 = 75
Number of more wafers in Container E than Container F at first
= 9 u - 5 u
= 4 u
= 4 x 75
= 300
Answer(s): 300