The ratio of the number of tarts in Container V to the number of tarts in Container W was 7 : 3. 10% of the tarts in Container V and 0.7 of those in Container W were peach. After transferring the tarts between the 2 containers, the number of chocolate tarts in both containers are the same. Likewise, the number of peach tarts in both containers are the same. If a total of 170 tarts were moved, how many more tarts were there in Container V than Container W at first?
Container V |
Container W |
7 u |
3 u |
Peach |
Chocolate |
Peach |
Chocolate |
0.7 u |
6.3 u |
2.1 u |
0.9 u |
+ 0.7 u |
- 2.7 u |
- 0.7 u |
+ 2.7 u |
1.4 u |
3.6 u |
1.4 u |
3.6 u |
Number of peach tarts in Container V
= 10% x 7 u
=
10100 x 7 u
= 0.7 u
Number of chocolate tarts in Container V
= 7 u - 0.7 u
= 6.3 u
Number of peach tarts in Container W
= 0.7 x 3 u
= 2.1 u
Number of chocolate tarts in Container W
= 3 u - 2.1 u
= 0.9 u
Number of peach tarts in each container in the end
= (0.7 u + 2.1 u) ÷ 2
= 2.8 u ÷ 2
= 1.4 u
Number of chocolate tarts in each container in the end
= (6.3 u + 0.9 u) ÷ 2
= 7.2 u ÷ 2
= 3.6 u
Number of tarts moved
= 0.7 u + 2.7 u
= 3.4 u
3.4 u = 170
1 u = 170 ÷ 3.4 = 50
Number of more tarts in Container V than Container W at first
= 7 u - 3 u
= 4 u
= 4 x 50
= 200
Answer(s): 200