A fruit seller sells only pomegranates and mangosteens. The ratio of pomegranates to mangosteens is 2 : 3. A total of 121 fruits are added. The number of pomegranates becomes 2 times as many as before and the number of mangosteens becomes 4 times as many as before. How many fruits are there at first?
|
Comparing pomegranates at first and in the end |
Pomegranates |
Mangosteens |
Comparing mangosteens at first and in the end |
Before |
1x2 = 2 u |
2 u |
3 u |
1x3 = 3 u |
Change |
|
+ 121 |
|
After |
2x2 = 4 u |
4 u |
12 u |
4x3 = 12 u |
The number of mangosteens at first is repeated. Make the number of mangosteens at first the same. LCM of 1 and 3 is 3.
The number of pomegranates at first is repeated. Make the number of pomegranates at first the same. LCM of 1 and 2 is 2.
Number of fruits at first
= 2 u + 3 u
= 5 u
Number of fruits in the end
= 4 u + 12 u
= 16 u
Number of fruits added
= 16 u - 5 u
= 11 u
11 u = 121
1 u = 121 ÷ 11 = 11
Number of fruits at first
= 5 u
= 5 x 11
= 55
Answer(s): 55