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 4 : 1. In Box F, the ratio of the number of apples to the number of oranges was 3 : 2. There were 2 times as many fruits in Box E as in Box F. After another 21 oranges were put into Box F, the ratio of the number of apples to the number of oranges in Box F became 1 : 3. How many fruits were there in Box E?
Box E |
Box F |
2x5 = 10 u |
1x5 = 5 u |
Apples |
Oranges |
Apples |
Oranges |
4x2 |
1x2 |
3 |
2 |
8 u |
2 u |
3 u |
2 u |
The total number of fruits in Box E is repeated. Make the total number of fruits in Box E the same. LCM of 2 and 5 is 10.
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 5 is 5.
|
Box E |
Box F |
|
Apples |
Oranges |
Apples |
Oranges |
Before |
8 u |
2 u |
3 u |
2 u |
Change |
|
|
|
+ 21 |
After
|
8 u
|
2 u
|
1x3 = 3 u |
3x3 = 9 u |
Number of apples in Box F remains unchanged. Make the number of apples in Box F the same. LCM of 3 and 1 is 3.
Number of oranges put into Box F
= 9 u - 2 u
= 7 u
7 u = 21
1 u = 21 ÷ 7 = 3
Number of fruits in Box E
= 8 u + 2 u
= 10 u
= 10 x 3
= 30
Answer(s): 30