A fruit seller sells only mangosteens and dragonfruits. The ratio of mangosteens to dragonfruits is 1 : 3. A total of 70 fruits are added. The number of mangosteens becomes 3 times as many as before and the number of dragonfruits becomes 2 times as many as before. How many fruits are there in the end?
|
Comparing mangosteens at first and in the end |
Mangosteens |
Dragonfruits |
Comparing dragonfruits at first and in the end |
Before |
1x1 = 1 u |
1 u |
3 u |
1x3 = 3 u |
Change |
|
+ 70 |
|
After |
3x1 = 3 u |
3 u |
6 u |
2x3 = 6 u |
The number of dragonfruits at first is repeated. Make the number of dragonfruits at first the same. LCM of 1 and 3 is 3.
The number of mangosteens at first is repeated. Make the number of mangosteens at first the same. LCM of 1 and 1 is 1.
Number of fruits at first
= 1 u + 3 u
= 4 u
Number of fruits in the end
= 3 u + 6 u
= 9 u
Number of fruits added
= 9 u - 4 u
= 5 u
5 u = 70
1 u = 70 ÷ 5 = 14
Number of fruits in the end
= 9 u
= 9 x 14
= 126
Answer(s): 126