The ratio of the number of puffs in Container W to the number of puffs in Container X was 5 : 3. 40% of the puffs in Container W and 0.8 of those in Container X were butter cream. After transferring the puffs between the 2 containers, the number of matcha puffs in both containers are the same. Likewise, the number of butter cream puffs in both containers are the same. If a total of 245 puffs were moved, how many more puffs were there in Container W than Container X at first?
Container W |
Container X |
5 u |
3 u |
Butter Cream |
Matcha |
Butter Cream |
Matcha |
2 u |
3 u |
2.4 u |
0.6 u |
+ 0.2 u |
- 1.2 u |
- 0.2 u |
+ 1.2 u |
2.2 u |
1.8 u |
2.2 u |
1.8 u |
Number of butter cream puffs in Container W
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of matcha puffs in Container W
= 5 u - 2 u
= 3 u
Number of butter cream puffs in Container X
= 0.8 x 3 u
= 2.4 u
Number of matcha puffs in Container X
= 3 u - 2.4 u
= 0.6 u
Number of butter cream puffs in each container in the end
= (2 u + 2.4 u) ÷ 2
= 4.4 u ÷ 2
= 2.2 u
Number of matcha puffs in each container in the end
= (3 u + 0.6 u) ÷ 2
= 3.6 u ÷ 2
= 1.8 u
Number of puffs moved
= 0.2 u + 1.2 u
= 1.4 u
1.4 u = 245
1 u = 245 ÷ 1.4 = 175
Number of more puffs in Container W than Container X at first
= 5 u - 3 u
= 2 u
= 2 x 175
= 350
Answer(s): 350