There were some apples and oranges in Box E and Box F. In Box E, the ratio of the apples to the number of oranges was 5 : 1. In Box F, the ratio of the number of apples to the number of oranges was 5 : 3. There were 3 times as many fruits in Box E as in Box F. After another 119 oranges were put into Box F, the ratio of the number of apples to the number of oranges in Box F became 1 : 4. How many fruits were there in Box E?
Box E |
Box F |
3x8 = 24 u |
1x8 = 8 u |
Apples |
Oranges |
Apples |
Oranges |
5x4 |
1x4 |
5 |
3 |
20 u |
4 u |
5 u |
3 u |
The total number of fruits in Box E is repeated. Make the total number of fruits in Box E the same. LCM of 3 and 6 is 24.
The total number of fruits in Box F at first is repeated. Make the total number of fruits in Box F the same. LCM of 1 and 8 is 8.
|
Box E |
Box F |
|
Apples |
Oranges |
Apples |
Oranges |
Before |
20 u |
4 u |
5 u |
3 u |
Change |
|
|
|
+ 119 |
After
|
20 u
|
4 u
|
1x5 = 5 u |
4x5 = 20 u |
Number of apples in Box F remains unchanged. Make the number of apples in Box F the same. LCM of 5 and 1 is 5.
Number of oranges put into Box F
= 20 u - 3 u
= 17 u
17 u = 119
1 u = 119 ÷ 17 = 7
Number of fruits in Box E
= 20 u + 4 u
= 24 u
= 24 x 7
= 168
Answer(s): 168