Risa had some kiwis and lemons in 2 crates. In Crate X, the number of kiwis to the number of lemons was in the ratio of 4 : 9. In Crate Y, there were four times as many kiwis as lemons. After Risa transferred
23 of the lemons from Crate X to Crate Y, the number of fruits left in Crate X was 133 and the ratio of the number of kiwis to the number of lemons in Crate B became 5 : 6. How many fruits were in Crate Y in the end?
|
Crate X |
Crate Y |
|
Kiwis |
Lemons |
Kiwis |
Lemons |
Before |
4 u |
9 u |
4x5 = 20 p |
1x5 = 5 p |
Change |
|
- 6 u |
|
+ 6 u (+ 19 p) |
After |
4 u |
3 u |
5x4 = 20 p |
6x4 = 24 p |
Number of lemons that Risa transferred from Crate X to Crate Y
=
23 x 9 u
= 6 u
Total number of fruits in Crate X in the end
= 4 u + 3 u
= 7 u
7 u = 133
1 u = 133 ÷ 7 = 19
The number of kiwis in Crate Y is the unchanged quantity.
LCM of 4 and 5 is 20.
Number of lemons that Risa transferred from Crate X to Crate Y
= 6 u
= 6 x 19
= 114
Increase in the number of lemons that due to the transfer from Crate X to Crate Y
= 24 p - 5 p
= 19 p
19 p = 6 u
19 p = 114
1 p = 114 ÷ 19 = 6
Number of fruits in Crate Y in the end
= 20 p + 24 p
= 44 p
= 44 x 6
= 264
Answer(s): 264