The ratio of the number of wafers in Container X to the number of wafers in Container Y was 5 : 3. 20% of the wafers in Container X and 0.6 of those in Container Y were strawberry. After transferring the wafers between the 2 containers, the number of matcha wafers in both containers are the same. Likewise, the number of strawberry wafers in both containers are the same. If a total of 198 wafers were moved, how many more wafers were there in Container X than Container Y at first?
Container X |
Container Y |
5 u |
3 u |
Strawberry |
Matcha |
Strawberry |
Matcha |
1 u |
4 u |
1.8 u |
1.2 u |
+ 0.4 u |
- 1.4 u |
- 0.4 u |
+ 1.4 u |
1.4 u |
2.6 u |
1.4 u |
2.6 u |
Number of strawberry wafers in Container X
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of matcha wafers in Container X
= 5 u - 1 u
= 4 u
Number of strawberry wafers in Container Y
= 0.6 x 3 u
= 1.8 u
Number of matcha wafers in Container Y
= 3 u - 1.8 u
= 1.2 u
Number of strawberry wafers in each container in the end
= (1 u + 1.8 u) ÷ 2
= 2.8 u ÷ 2
= 1.4 u
Number of matcha wafers in each container in the end
= (4 u + 1.2 u) ÷ 2
= 5.2 u ÷ 2
= 2.6 u
Number of wafers moved
= 0.4 u + 1.4 u
= 1.8 u
1.8 u = 198
1 u = 198 ÷ 1.8 = 110
Number of more wafers in Container X than Container Y at first
= 5 u - 3 u
= 2 u
= 2 x 110
= 220
Answer(s): 220