The ratio of the number of wafers in Container W to the number of wafers in Container X was 7 : 3. 20% of the wafers in Container W and 0.8 of those in Container X were vanilla. After transferring the wafers between the 2 containers, the number of chocolate wafers in both containers are the same. Likewise, the number of vanilla wafers in both containers are the same. If a total of 192 wafers were moved, how many more wafers were there in Container W than Container X at first?
Container W |
Container X |
7 u |
3 u |
Vanilla |
Chocolate |
Vanilla |
Chocolate |
1.4 u |
5.6 u |
2.4 u |
0.6 u |
+ 0.5 u |
- 2.5 u |
- 0.5 u |
+ 2.5 u |
1.9 u |
3.1 u |
1.9 u |
3.1 u |
Number of vanilla wafers in Container W
= 20% x 7 u
=
20100 x 7 u
= 1.4 u
Number of chocolate wafers in Container W
= 7 u - 1.4 u
= 5.6 u
Number of vanilla wafers in Container X
= 0.8 x 3 u
= 2.4 u
Number of chocolate wafers in Container X
= 3 u - 2.4 u
= 0.6 u
Number of vanilla wafers in each container in the end
= (1.4 u + 2.4 u) ÷ 2
= 3.8 u ÷ 2
= 1.9 u
Number of chocolate wafers in each container in the end
= (5.6 u + 0.6 u) ÷ 2
= 6.2 u ÷ 2
= 3.1 u
Number of wafers moved
= 0.5 u + 2.5 u
= 3 u
3 u = 192
1 u = 192 ÷ 3 = 64
Number of more wafers in Container W than Container X at first
= 7 u - 3 u
= 4 u
= 4 x 64
= 256
Answer(s): 256