There were some mangosteens and oranges in Box K and Box L. In Box K, the ratio of the mangosteens to the number of oranges was 3 : 1. In Box L, the ratio of the number of mangosteens to the number of oranges was 3 : 1. There were 2 times as many fruits in Box K as in Box L. After another 99 oranges were put into Box L, the ratio of the number of mangosteens to the number of oranges in Box L became 1 : 4. How many fruits were there in Box K?
| Box K |
Box L |
2x4 =
8 u |
1x4 =
4 u |
| Mangosteens |
Oranges |
Mangosteens |
Oranges |
| 3x2 |
1x2 |
3 |
1 |
| 6 u |
2 u |
3 u |
1 u |
The total number of fruits in Box K is repeated. Make the total number of fruits in Box K the same. LCM of 2 and 4 is 8.
The total number of fruits in Box L at first is repeated. Make the total number of fruits in Box L the same. LCM of 1 and 4 is 4.
| |
Box K |
Box L |
| |
Mangosteens |
Oranges |
Mangosteens |
Oranges |
| Before |
6 u |
2 u |
3 u |
1 u |
| Change |
|
|
|
+ 99 |
After
|
6 u
|
2 u
|
1x3 =
3 u |
4x3 =
12 u |
Number of mangosteens in Box L remains unchanged. Make the number of mangosteens in Box L the same. LCM of 3 and 1 is 3.
Number of oranges put into Box L
= 12 u - 1 u
= 11 u
11 u = 99
1 u = 99 ÷ 11 = 9
Number of fruits in Box K
= 6 u + 2 u
= 8 u
= 8 x 9
= 72
Answer(s): 72
