The ratio of the number of wafers in Container M to the number of wafers in Container N was 5 : 3. 10% of the wafers in Container M and 0.7 of those in Container N were matcha. After transferring the wafers between the 2 containers, the number of strawberry wafers in both containers are the same. Likewise, the number of matcha wafers in both containers are the same. If a total of 299 wafers were moved, how many more wafers were there in Container M than Container N at first?
Container M |
Container N |
5 u |
3 u |
Matcha |
Strawberry |
Matcha |
Strawberry |
0.5 u |
4.5 u |
2.1 u |
0.9 u |
+ 0.8 u |
- 1.8 u |
- 0.8 u |
+ 1.8 u |
1.3 u |
2.7 u |
1.3 u |
2.7 u |
Number of matcha wafers in Container M
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
Number of strawberry wafers in Container M
= 5 u - 0.5 u
= 4.5 u
Number of matcha wafers in Container N
= 0.7 x 3 u
= 2.1 u
Number of strawberry wafers in Container N
= 3 u - 2.1 u
= 0.9 u
Number of matcha wafers in each container in the end
= (0.5 u + 2.1 u) ÷ 2
= 2.6 u ÷ 2
= 1.3 u
Number of strawberry wafers in each container in the end
= (4.5 u + 0.9 u) ÷ 2
= 5.4 u ÷ 2
= 2.7 u
Number of wafers moved
= 0.8 u + 1.8 u
= 2.6 u
2.6 u = 299
1 u = 299 ÷ 2.6 = 115
Number of more wafers in Container M than Container N at first
= 5 u - 3 u
= 2 u
= 2 x 115
= 230
Answer(s): 230