The ratio of the number of wafers in Container P to the number of wafers in Container Q was 7 : 3. 30% of the wafers in Container P and 0.9 of those in Container Q were cherry. After transferring the wafers between the 2 containers, the number of chocolate wafers in both containers are the same. Likewise, the number of cherry wafers in both containers are the same. If a total of 156 wafers were moved, how many more wafers were there in Container P than Container Q at first?
Container P |
Container Q |
7 u |
3 u |
Cherry |
Chocolate |
Cherry |
Chocolate |
2.1 u |
4.9 u |
2.7 u |
0.3 u |
+ 0.3 u |
- 2.3 u |
- 0.3 u |
+ 2.3 u |
2.4 u |
2.6 u |
2.4 u |
2.6 u |
Number of cherry wafers in Container P
= 30% x 7 u
=
30100 x 7 u
= 2.1 u
Number of chocolate wafers in Container P
= 7 u - 2.1 u
= 4.9 u
Number of cherry wafers in Container Q
= 0.9 x 3 u
= 2.7 u
Number of chocolate wafers in Container Q
= 3 u - 2.7 u
= 0.3 u
Number of cherry wafers in each container in the end
= (2.1 u + 2.7 u) ÷ 2
= 4.8 u ÷ 2
= 2.4 u
Number of chocolate wafers in each container in the end
= (4.9 u + 0.3 u) ÷ 2
= 5.2 u ÷ 2
= 2.6 u
Number of wafers moved
= 0.3 u + 2.3 u
= 2.6 u
2.6 u = 156
1 u = 156 ÷ 2.6 = 60
Number of more wafers in Container P than Container Q at first
= 7 u - 3 u
= 4 u
= 4 x 60
= 240
Answer(s): 240