There were 122 persimmons and mangosteens altogether. After
56 of the persimmons and half of the mangosteens were given away, there were a total of 31 persimmons and mangosteens left. What fraction of the fruits were mangosteens at first? Give your answer in its simplest form.
| |
Persimmons |
Mangosteens |
Total |
| Before |
6 u |
2 p |
122 |
| Change |
- 5 u |
- 1 p |
- 91 |
| After |
1 u |
1 p |
31 |
Number of persimmons and mangosteens given away
= 122 - 31
= 91
5 u + 1 p = 91
1 p = 91 - 5 u --- (1)
1 u + 1 p = 31
1 p = 31 - 1 u --- (2)
(2) = (1)
31 - 1 u = 91 - 5 u
5 u - 1 u = 91 - 31
4 u = 60
1 u = 60 ÷ 4 = 15
Number of persimmons at first
= 6 u
= 6 x 15
= 90
Number of mangosteens at first
= 122 - 90
= 32
Fraction of the fruits that were mangosteens at first
=
32122 =
1661 Answer(s):
1661 
