The ratio of the number of wafers in Container U to the number of wafers in Container V was 7 : 5. 40% of the wafers in Container U and 0.6 of those in Container V were vanilla. After transferring the wafers between the 2 containers, the number of matcha wafers in both containers are the same. Likewise, the number of vanilla wafers in both containers are the same. If a total of 168 wafers were moved, how many more wafers were there in Container U than Container V at first?
Container U |
Container V |
7 u |
5 u |
Vanilla |
Matcha |
Vanilla |
Matcha |
2.8 u |
4.2 u |
3 u |
2 u |
+ 0.1 u |
- 1.1 u |
- 0.1 u |
+ 1.1 u |
2.9 u |
3.1 u |
2.9 u |
3.1 u |
Number of vanilla wafers in Container U
= 40% x 7 u
=
40100 x 7 u
= 2.8 u
Number of matcha wafers in Container U
= 7 u - 2.8 u
= 4.2 u
Number of vanilla wafers in Container V
= 0.6 x 5 u
= 3 u
Number of matcha wafers in Container V
= 5 u - 3 u
= 2 u
Number of vanilla wafers in each container in the end
= (2.8 u + 3 u) ÷ 2
= 5.8 u ÷ 2
= 2.9 u
Number of matcha wafers in each container in the end
= (4.2 u + 2 u) ÷ 2
= 6.2 u ÷ 2
= 3.1 u
Number of wafers moved
= 0.1 u + 1.1 u
= 1.2 u
1.2 u = 168
1 u = 168 ÷ 1.2 = 140
Number of more wafers in Container U than Container V at first
= 7 u - 5 u
= 2 u
= 2 x 140
= 280
Answer(s): 280