The ratio of the number of wafers in Container L to the number of wafers in Container M was 5 : 3. 40% of the wafers in Container L and 0.8 of those in Container M were cherry. After transferring the wafers between the 2 containers, the number of matcha wafers in both containers are the same. Likewise, the number of cherry wafers in both containers are the same. If a total of 161 wafers were moved, how many more wafers were there in Container L than Container M at first?
Container L |
Container M |
5 u |
3 u |
Cherry |
Matcha |
Cherry |
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 cherry wafers in Container L
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of matcha wafers in Container L
= 5 u - 2 u
= 3 u
Number of cherry wafers in Container M
= 0.8 x 3 u
= 2.4 u
Number of matcha wafers in Container M
= 3 u - 2.4 u
= 0.6 u
Number of cherry wafers in each container in the end
= (2 u + 2.4 u) ÷ 2
= 4.4 u ÷ 2
= 2.2 u
Number of matcha wafers in each container in the end
= (3 u + 0.6 u) ÷ 2
= 3.6 u ÷ 2
= 1.8 u
Number of wafers moved
= 0.2 u + 1.2 u
= 1.4 u
1.4 u = 161
1 u = 161 ÷ 1.4 = 115
Number of more wafers in Container L than Container M at first
= 5 u - 3 u
= 2 u
= 2 x 115
= 230
Answer(s): 230