The ratio of the number of wafers in Container M to the number of wafers in Container N was 5 : 3. 30% of the wafers in Container M and 0.7 of those in Container N were cherry. After transferring the wafers between the 2 boxes, the number of strawberry wafers in both boxes are the same. Likewise, the number of cherry wafers in both boxes are the same. If a total of 192 wafers were moved, how many more wafers were there in Container M than Container N at first?
Container M |
Container N |
5 u |
3 u |
Cherry |
Strawberry |
Cherry |
Strawberry |
1.5 u |
3.5 u |
2.1 u |
0.9 u |
+ 0.3 u |
- 1.3 u |
- 0.3 u |
+ 1.3 u |
1.8 u |
2.2 u |
1.8 u |
2.2 u |
Number of cherry wafers in Container M
= 30% x 5 u
=
30100 x 5 u
= 1.5 u
Number of strawberry wafers in Container M
= 5 u - 1.5 u
= 3.5 u
Number of cherry wafers in Container N
= 0.7 x 3 u
= 2.1 u
Number of strawberry wafers in Container N
= 3 u - 2.1 u
= 0.9 u
Number of cherry wafers in each box in the end
= (1.5 u + 2.1 u) ÷ 2
= 3.6 u ÷ 2
= 1.8 u
Number of strawberry wafers in each box in the end
= (3.5 u + 0.9 u) ÷ 2
= 4.4 u ÷ 2
= 2.2 u
Number of wafers moved
= 0.3 u + 1.3 u
= 1.6 u
1.6 u = 192
1 u = 192 ÷ 1.6 = 120
Number of more wafers in Container M than Container N at first
= 5 u - 3 u
= 2 u
= 2 x 120
= 240
Answer(s): 240