The ratio of the number of biscuits in Container W to the number of biscuits in Container X was 5 : 3. 40% of the biscuits in Container W and 0.7 of those in Container X were cherry. After transferring the biscuits between the 2 boxes, the number of strawberry biscuits in both boxes are the same. Likewise, the number of cherry biscuits in both boxes are the same. If a total of 154 biscuits were moved, how many more biscuits were there in Container W than Container X at first?
Container W |
Container X |
5 u |
3 u |
Cherry |
Strawberry |
Cherry |
Strawberry |
2 u |
3 u |
2.1 u |
0.9 u |
+ 0.05 u |
- 1.05 u |
- 0.05 u |
+ 1.05 u |
2.05 u |
1.95 u |
2.05 u |
1.95 u |
Number of cherry biscuits in Container W
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of strawberry biscuits in Container W
= 5 u - 2 u
= 3 u
Number of cherry biscuits in Container X
= 0.7 x 3 u
= 2.1 u
Number of strawberry biscuits in Container X
= 3 u - 2.1 u
= 0.9 u
Number of cherry biscuits in each box in the end
= (2 u + 2.1 u) ÷ 2
= 4.1 u ÷ 2
= 2.05 u
Number of strawberry biscuits in each box in the end
= (3 u + 0.9 u) ÷ 2
= 3.9 u ÷ 2
= 1.95 u
Number of biscuits moved
= 0.05 u + 1.05 u
= 1.1 u
1.1 u = 154
1 u = 154 ÷ 1.1 = 140
Number of more biscuits in Container W than Container X at first
= 5 u - 3 u
= 2 u
= 2 x 140
= 280
Answer(s): 280