The ratio of the number of tarts in Container V to the number of tarts in Container W was 9 : 5. 30% of the tarts in Container V and 0.7 of those in Container W were mango. After transferring the tarts between the 2 containers, the number of chocolate tarts in both containers are the same. Likewise, the number of mango tarts in both containers are the same. If a total of 210 tarts were moved, how many more tarts were there in Container V than Container W at first?
Container V |
Container W |
9 u |
5 u |
Mango |
Chocolate |
Mango |
Chocolate |
2.7 u |
6.3 u |
3.5 u |
1.5 u |
+ 0.4 u |
- 2.4 u |
- 0.4 u |
+ 2.4 u |
3.1 u |
3.9 u |
3.1 u |
3.9 u |
Number of mango tarts in Container V
= 30% x 9 u
=
30100 x 9 u
= 2.7 u
Number of chocolate tarts in Container V
= 9 u - 2.7 u
= 6.3 u
Number of mango tarts in Container W
= 0.7 x 5 u
= 3.5 u
Number of chocolate tarts in Container W
= 5 u - 3.5 u
= 1.5 u
Number of mango tarts in each container in the end
= (2.7 u + 3.5 u) ÷ 2
= 6.2 u ÷ 2
= 3.1 u
Number of chocolate tarts in each container in the end
= (6.3 u + 1.5 u) ÷ 2
= 7.8 u ÷ 2
= 3.9 u
Number of tarts moved
= 0.4 u + 2.4 u
= 2.8 u
2.8 u = 210
1 u = 210 ÷ 2.8 = 75
Number of more tarts in Container V than Container W at first
= 9 u - 5 u
= 4 u
= 4 x 75
= 300
Answer(s): 300